Write The Equation Of The Line With The Following Slope And { Y $} − I N T E R C E P T : -intercept: − In T Erce Pt : {$ M = 7 $}$, { (0, -4) $}$The Equation Of The Line Is { \square$}$.(Type Your Answer In Slope-intercept Form. Use Integers Or
Understanding the Problem
The problem requires us to find the equation of a line with a given slope and y-intercept. The slope of the line is 7, and the y-intercept is -4. We need to use this information to write the equation of the line in slope-intercept form.
Recalling the Slope-Intercept Form
The slope-intercept form of a line is given by the equation:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
Using the Given Information
We are given that the slope of the line is 7, so we can substitute this value into the equation:
y = 7x + b
We are also given that the y-intercept is -4, so we can substitute this value into the equation:
y = 7x - 4
The Equation of the Line
Now that we have substituted the given values into the equation, we can see that the equation of the line is:
y = 7x - 4
This is the equation of the line with the given slope and y-intercept.
Interpreting the Equation
The equation y = 7x - 4 tells us that the line has a slope of 7, which means that for every 1 unit we move to the right, the line will rise by 7 units. The y-intercept of -4 tells us that the line crosses the y-axis at the point (0, -4).
Example Use Case
Suppose we want to find the y-coordinate of the point on the line that is 2 units to the right of the y-axis. We can substitute x = 2 into the equation:
y = 7(2) - 4 y = 14 - 4 y = 10
So, the y-coordinate of the point on the line that is 2 units to the right of the y-axis is 10.
Conclusion
In this article, we have seen how to find the equation of a line with a given slope and y-intercept. We have used the slope-intercept form of a line and substituted the given values into the equation to find the equation of the line. We have also interpreted the equation and seen how to use it to find the y-coordinate of a point on the line.
Key Takeaways
- The slope-intercept form of a line is given by the equation y = mx + b.
- The equation of a line with a given slope and y-intercept can be found by substituting the given values into the equation.
- The equation of a line can be used to find the y-coordinate of a point on the line.
Further Reading
For more information on the slope-intercept form of a line and how to use it to find the equation of a line, see the following resources:
Glossary
- Slope: A measure of how steep a line is. It is calculated as the ratio of the vertical change to the horizontal change.
- Y-Intercept: The point at which a line crosses the y-axis. It is the value of y when x is equal to 0.
- Slope-Intercept Form: A way of writing the equation of a line. It is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
Frequently Asked Questions (FAQs) about the Equation of a Line ================================================================
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: How do I find the equation of a line with a given slope and y-intercept?
A: To find the equation of a line with a given slope and y-intercept, you can substitute the given values into the slope-intercept form of a line. For example, if the slope is 7 and the y-intercept is -4, the equation of the line would be y = 7x - 4.
Q: What is the y-intercept of a line?
A: The y-intercept of a line is the point at which the line crosses the y-axis. It is the value of y when x is equal to 0.
Q: How do I find the y-coordinate of a point on a line?
A: To find the y-coordinate of a point on a line, you can substitute the x-coordinate of the point into the equation of the line. For example, if the equation of the line is y = 7x - 4 and the x-coordinate of the point is 2, the y-coordinate of the point would be y = 7(2) - 4 = 10.
Q: What is the slope of a line?
A: The slope of a line is a measure of how steep the line is. It is calculated as the ratio of the vertical change to the horizontal change.
Q: How do I calculate the slope of a line?
A: To calculate the slope of a line, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Q: What is the equation of a horizontal line?
A: The equation of a horizontal line is given by the equation y = b, where b is the y-intercept of the line.
Q: What is the equation of a vertical line?
A: The equation of a vertical line is given by the equation x = a, where a is the x-intercept of the line.
Q: How do I graph a line?
A: To graph a line, you can use a coordinate plane and plot two points on the line. Then, draw a line through the two points to represent the line.
Q: What is the difference between a linear equation and a nonlinear equation?
A: A linear equation is an equation in which the highest power of the variable is 1. A nonlinear equation is an equation in which the highest power of the variable is greater than 1.
Q: How do I solve a linear equation?
A: To solve a linear equation, you can use the following steps:
- Simplify the equation by combining like terms.
- Isolate the variable by adding or subtracting the same value to both sides of the equation.
- Solve for the variable by dividing both sides of the equation by the coefficient of the variable.
Q: What is the equation of a line with a given slope and x-intercept?
A: To find the equation of a line with a given slope and x-intercept, you can use the point-slope form of a line. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Q: How do I find the equation of a line with a given slope and x-intercept?
A: To find the equation of a line with a given slope and x-intercept, you can substitute the given values into the point-slope form of a line. For example, if the slope is 7 and the x-intercept is 2, the equation of the line would be y - (-4) = 7(x - 2).
Q: What is the equation of a line with a given slope and y-intercept and x-intercept?
A: To find the equation of a line with a given slope and y-intercept and x-intercept, you can use the slope-intercept form of a line and the point-slope form of a line. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Q: How do I find the equation of a line with a given slope and y-intercept and x-intercept?
A: To find the equation of a line with a given slope and y-intercept and x-intercept, you can substitute the given values into the slope-intercept form of a line and the point-slope form of a line. For example, if the slope is 7, the y-intercept is -4, and the x-intercept is 2, the equation of the line would be y = 7x - 4 and y - (-4) = 7(x - 2).
Q: What is the equation of a line with a given slope and two points?
A: To find the equation of a line with a given slope and two points, you can use the point-slope form of a line. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) and (x2, y2) are two points on the line and m is the slope of the line.
Q: How do I find the equation of a line with a given slope and two points?
A: To find the equation of a line with a given slope and two points, you can substitute the given values into the point-slope form of a line. For example, if the slope is 7, the two points are (2, 3) and (4, 5), the equation of the line would be y - 3 = 7(x - 2).
Q: What is the equation of a line with a given slope and a point and a line?
A: To find the equation of a line with a given slope and a point and a line, you can use the point-slope form of a line and the equation of the line. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. The equation of the line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: How do I find the equation of a line with a given slope and a point and a line?
A: To find the equation of a line with a given slope and a point and a line, you can substitute the given values into the point-slope form of a line and the equation of the line. For example, if the slope is 7, the point is (2, 3), and the equation of the line is y = 2x + 1, the equation of the line would be y - 3 = 7(x - 2).
Q: What is the equation of a line with a given slope and a point and a line and a point?
A: To find the equation of a line with a given slope and a point and a line and a point, you can use the point-slope form of a line, the equation of the line, and the point. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. The equation of the line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: How do I find the equation of a line with a given slope and a point and a line and a point?
A: To find the equation of a line with a given slope and a point and a line and a point, you can substitute the given values into the point-slope form of a line, the equation of the line, and the point. For example, if the slope is 7, the point is (2, 3), the equation of the line is y = 2x + 1, and the point is (4, 5), the equation of the line would be y - 3 = 7(x - 2).
Q: What is the equation of a line with a given slope and a point and a line and a point and a line?
A: To find the equation of a line with a given slope and a point and a line and a point and a line, you can use the point-slope form of a line, the equation of the line, the point, and the line. The point-slope form of a line is given by the equation y - y1