Find The Slope And \[$y\$\]-intercept Of The Following Linear Equation. Express The \[$y\$\]-intercept As A Coordinate Pair.$\[ Y = 5x \\]Answer: Slope: \[$\square\$\] \[$y\$\]-Intercept: \[$\square\$\]
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Introduction
In mathematics, a linear equation is a type of equation in which the highest power of the variable(s) is 1. It can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope represents the rate of change of the variable, while the y-intercept represents the point at which the line intersects the y-axis. In this article, we will learn how to find the slope and y-intercept of a linear equation.
What is a Linear Equation?
A linear equation is a type of equation in which the highest power of the variable(s) is 1. It can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope represents the rate of change of the variable, while the y-intercept represents the point at which the line intersects the y-axis.
Example of a Linear Equation
y = 5x
In this example, the linear equation is y = 5x. To find the slope and y-intercept, we need to identify the values of m and b.
Finding the Slope
The slope of a linear equation is represented by the value of m. To find the slope, we need to look at the coefficient of the variable (x). In this case, the coefficient of x is 5, which means that the slope is 5.
Formula for Finding the Slope
m = coefficient of x
In this case, the coefficient of x is 5, so the slope is 5.
Finding the y-Intercept
The y-intercept of a linear equation is represented by the value of b. To find the y-intercept, we need to look at the constant term in the equation. In this case, the constant term is 0, which means that the y-intercept is (0, 0).
Formula for Finding the y-Intercept
b = constant term
In this case, the constant term is 0, so the y-intercept is (0, 0).
Conclusion
In conclusion, the slope of the linear equation y = 5x is 5, and the y-intercept is (0, 0). The slope represents the rate of change of the variable, while the y-intercept represents the point at which the line intersects the y-axis.
Final Answer
Slope: 5 y-Intercept: (0, 0)
Discussion
- What is a linear equation?
- How do you find the slope of a linear equation?
- How do you find the y-intercept of a linear equation?
Related Topics
- Graphing linear equations
- Writing linear equations in slope-intercept form
- Finding the equation of a line given two points
References
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Q: What is a linear equation?
A: A linear equation is a type of equation in which the highest power of the variable(s) is 1. It can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.
Q: How do I find the slope of a linear equation?
A: To find the slope of a linear equation, you need to look at the coefficient of the variable (x). The slope is equal to the coefficient of x.
Example
y = 5x
In this case, the coefficient of x is 5, so the slope is 5.
Q: How do I find the y-intercept of a linear equation?
A: To find the y-intercept of a linear equation, you need to look at the constant term in the equation. The y-intercept is equal to the constant term.
Example
y = 5x
In this case, the constant term is 0, so the y-intercept is (0, 0).
Q: What is the difference between the slope and y-intercept?
A: The slope represents the rate of change of the variable, while the y-intercept represents the point at which the line intersects the y-axis.
Q: Can I have a negative slope?
A: Yes, you can have a negative slope. A negative slope means that the line is sloping downward from left to right.
Example
y = -5x
In this case, the slope is -5, which means that the line is sloping downward from left to right.
Q: Can I have a zero slope?
A: Yes, you can have a zero slope. A zero slope means that the line is horizontal.
Example
y = 0x
In this case, the slope is 0, which means that the line is horizontal.
Q: Can I have a fractional slope?
A: Yes, you can have a fractional slope. A fractional slope means that the line is sloping upward or downward at a rate that is not a whole number.
Example
y = (1/2)x
In this case, the slope is 1/2, which means that the line is sloping upward at a rate of 1/2.
Q: Can I have a negative y-intercept?
A: Yes, you can have a negative y-intercept. A negative y-intercept means that the line intersects the y-axis below the x-axis.
Example
y = 5x - 3
In this case, the y-intercept is -3, which means that the line intersects the y-axis below the x-axis.
Q: Can I have a fractional y-intercept?
A: Yes, you can have a fractional y-intercept. A fractional y-intercept means that the line intersects the y-axis at a point that is not a whole number.
Example
y = (1/2)x + 1/3
In this case, the y-intercept is 1/3, which means that the line intersects the y-axis at a point that is not a whole number.
Q: How do I graph a linear equation?
A: To graph a linear equation, you need to plot two points on the coordinate plane and draw a line through them.
Example
y = 5x
To graph this equation, you need to plot two points on the coordinate plane and draw a line through them.
Q: How do I write a linear equation in slope-intercept form?
A: To write a linear equation in slope-intercept form, you need to rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Example
y = 5x + 3
In this case, the equation is already in slope-intercept form, with a slope of 5 and a y-intercept of 3.
Q: How do I find the equation of a line given two points?
A: To find the equation of a line given two points, you need to use the slope formula to find the slope of the line, and then use the point-slope form to write the equation of the line.
Example
Points: (2, 3) and (4, 5)
To find the equation of the line, you need to use the slope formula to find the slope of the line, and then use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given the slope and a point?
A: To find the equation of a line given the slope and a point, you need to use the point-slope form to write the equation of the line.
Example
Slope: 5, Point: (2, 3)
To find the equation of the line, you need to use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given two parallel lines?
A: To find the equation of a line given two parallel lines, you need to use the slope formula to find the slope of the line, and then use the point-slope form to write the equation of the line.
Example
Lines: y = 5x + 3 and y = 5x - 2
To find the equation of the line, you need to use the slope formula to find the slope of the line, and then use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given two perpendicular lines?
A: To find the equation of a line given two perpendicular lines, you need to use the slope formula to find the slope of the line, and then use the point-slope form to write the equation of the line.
Example
Lines: y = 5x + 3 and y = -1/5x - 2
To find the equation of the line, you need to use the slope formula to find the slope of the line, and then use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given a point and a line parallel to it?
A: To find the equation of a line given a point and a line parallel to it, you need to use the point-slope form to write the equation of the line.
Example
Point: (2, 3), Line: y = 5x + 3
To find the equation of the line, you need to use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given a point and a line perpendicular to it?
A: To find the equation of a line given a point and a line perpendicular to it, you need to use the point-slope form to write the equation of the line.
Example
Point: (2, 3), Line: y = -1/5x - 2
To find the equation of the line, you need to use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given a point and a line that passes through it?
A: To find the equation of a line given a point and a line that passes through it, you need to use the point-slope form to write the equation of the line.
Example
Point: (2, 3), Line: y = 5x + 3
To find the equation of the line, you need to use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given a point and a line that is parallel to it?
A: To find the equation of a line given a point and a line that is parallel to it, you need to use the point-slope form to write the equation of the line.
Example
Point: (2, 3), Line: y = 5x + 3
To find the equation of the line, you need to use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given a point and a line that is perpendicular to it?
A: To find the equation of a line given a point and a line that is perpendicular to it, you need to use the point-slope form to write the equation of the line.
Example
Point: (2, 3), Line: y = -1/5x - 2
To find the equation of the line, you need to use the point-slope form to write the equation of the line.
Q: How do I find the equation of a line given a point and a line that passes through it and is parallel to it?
A: To find the equation of a line given a point and a line that passes through it and is parallel to it, you need to use the point-slope form to write the equation of the line.
Example
Point: (2, 3), Line: y = 5x + 3
To find the equation of the line, you need to use the point-slope form to write the equation of the line.