Provide The Equation For The Line In Slope-intercept Form: $y = -3x - 1$
The slope-intercept form of a line is a way to express the equation of a line in terms of its slope and y-intercept. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. In this article, we will explore the equation for the line in slope-intercept form, specifically the equation y = -3x - 1.
What is the Slope-Intercept Form of a Line?
The slope-intercept form of a line is a way to express the equation of a line in terms of its slope and y-intercept. The slope of a line is a measure of how steep it is, and it is represented by the letter m. The y-intercept of a line is the point where the line intersects the y-axis, and it is represented by the letter b. The equation y = mx + b represents a line that has a slope of m and a y-intercept of b.
The Equation y = -3x - 1
The equation y = -3x - 1 is a specific example of the slope-intercept form of a line. In this equation, the slope is -3 and the y-intercept is -1. This means that the line has a steepness of -3 and intersects the y-axis at the point (0, -1).
How to Interpret the Equation
To interpret the equation y = -3x - 1, we need to understand what the slope and y-intercept represent. The slope of -3 means that for every 1 unit increase in x, the value of y decreases by 3 units. This means that the line is sloping downward from left to right. The y-intercept of -1 means that the line intersects the y-axis at the point (0, -1), which is 1 unit below the origin.
Graphing the Line
To graph the line y = -3x - 1, we can use the slope and y-intercept to find two points on the line. We can then use these points to draw the line. Let's find two points on the line by plugging in different values of x.
- When x = 0, y = -3(0) - 1 = -1. This gives us the point (0, -1).
- When x = 1, y = -3(1) - 1 = -4. This gives us the point (1, -4).
We can use these two points to draw the line. The line will pass through the points (0, -1) and (1, -4), and it will have a slope of -3.
Solving for x
To solve for x, we can rearrange the equation y = -3x - 1 to isolate x. We can do this by adding 1 to both sides of the equation, which gives us y + 1 = -3x. We can then divide both sides of the equation by -3, which gives us x = -(y + 1)/3.
Solving for y
To solve for y, we can rearrange the equation y = -3x - 1 to isolate y. We can do this by adding 3x to both sides of the equation, which gives us y = -3x - 1. We can then add 1 to both sides of the equation, which gives us y + 1 = -3x.
Conclusion
In conclusion, the equation y = -3x - 1 is a specific example of the slope-intercept form of a line. The slope of -3 means that the line is sloping downward from left to right, and the y-intercept of -1 means that the line intersects the y-axis at the point (0, -1). We can graph the line by finding two points on the line and using these points to draw the line. We can also solve for x and y by rearranging the equation.
Frequently Asked Questions
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is a way to express the equation of a line in terms of its slope and y-intercept. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: What is the equation y = -3x - 1?
A: The equation y = -3x - 1 is a specific example of the slope-intercept form of a line. In this equation, the slope is -3 and the y-intercept is -1.
Q: How to interpret the equation y = -3x - 1?
A: To interpret the equation y = -3x - 1, we need to understand what the slope and y-intercept represent. The slope of -3 means that for every 1 unit increase in x, the value of y decreases by 3 units. This means that the line is sloping downward from left to right. The y-intercept of -1 means that the line intersects the y-axis at the point (0, -1).
Q: How to graph the line y = -3x - 1?
A: To graph the line y = -3x - 1, we can use the slope and y-intercept to find two points on the line. We can then use these points to draw the line.
Q: How to solve for x and y in the equation y = -3x - 1?
In this article, we will continue to explore the equation y = -3x - 1 and answer some frequently asked questions about it.
Q: What is the slope of the line y = -3x - 1?
A: The slope of the line y = -3x - 1 is -3. This means that for every 1 unit increase in x, the value of y decreases by 3 units.
Q: What is the y-intercept of the line y = -3x - 1?
A: The y-intercept of the line y = -3x - 1 is -1. This means that the line intersects the y-axis at the point (0, -1).
Q: How do I graph the line y = -3x - 1?
A: To graph the line y = -3x - 1, you can use the slope and y-intercept to find two points on the line. You can then use these points to draw the line.
Q: How do I find the x-intercept of the line y = -3x - 1?
A: To find the x-intercept of the line y = -3x - 1, you can set y = 0 and solve for x. This gives you the equation 0 = -3x - 1. You can then add 1 to both sides of the equation and divide both sides of the equation by -3 to get x = -1/3.
Q: How do I find the y-intercept of the line y = -3x - 1?
A: The y-intercept of the line y = -3x - 1 is already given as -1.
Q: How do I find the slope of the line y = -3x - 1?
A: The slope of the line y = -3x - 1 is already given as -3.
Q: How do I find the equation of the line y = -3x - 1 in point-slope form?
A: To find the equation of the line y = -3x - 1 in point-slope form, you can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, you can use the point (0, -1) and the slope -3 to get the equation y - (-1) = -3(x - 0), which simplifies to y + 1 = -3x.
Q: How do I find the equation of the line y = -3x - 1 in standard form?
A: To find the equation of the line y = -3x - 1 in standard form, you can use the standard form of a line, which is Ax + By = C, where A, B, and C are constants. In this case, you can rewrite the equation y = -3x - 1 as -3x + y = -1.
Q: How do I find the equation of the line y = -3x - 1 in slope-intercept form?
A: The equation of the line y = -3x - 1 is already given in slope-intercept form.
Q: How do I find the equation of the line y = -3x - 1 in parametric form?
A: To find the equation of the line y = -3x - 1 in parametric form, you can use the parametric equations x = t and y = -3t - 1, where t is a parameter.
Q: How do I find the equation of the line y = -3x - 1 in polar form?
A: To find the equation of the line y = -3x - 1 in polar form, you can use the polar equation r = (x^2 + y2)(1/2) and the equation y = -3x - 1 to get the equation r = (x^2 + (-3x - 1)2)(1/2).
Conclusion
In conclusion, the equation y = -3x - 1 is a specific example of the slope-intercept form of a line. We have answered some frequently asked questions about the equation and explored different ways to express the equation in different forms.