Lesson 6 Homework Practice Write Linear Equations Answer Key
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How to Write Linear Equations in Point-Slope and Slope-Intercept Forms
In this article, we will learn how to write linear equations in two different forms: point-slope form and slope-intercept form. These forms are useful for graphing lines, finding their slopes and intercepts, and solving systems of linear equations.
A linear equation is an equation that can be written in the form ax + by = c, where a, b, and c are constants and x and y are variables. A linear equation represents a straight line on a coordinate plane.
Point-Slope Form
The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is any point on the line. To write a linear equation in point-slope form, we need to know the slope of the line and one point on the line.
For example, suppose we want to write a linear equation that passes through the point (-5, 6) and has a slope of 3. We can plug these values into the point-slope form:
y - 6 = 3(x - (-5))
We can simplify this equation by distributing the 3 and adding 6 to both sides:
y = 3x + 21
Slope-Intercept Form
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, or the value of y when x = 0. To write a linear equation in slope-intercept form, we need to know the slope of the line and the y-intercept of the line.
For example, suppose we want to write a linear equation that passes through the point (0, 1) and has a slope of 2. We can plug these values into the slope-intercept form:
y = 2x + b
To find the value of b, we can substitute x = 0 and y = 1:
1 = 2(0) + bb = 1
Therefore, the equation in slope-intercept form is:
y = 2x + 1
Lesson 6 Homework Practice Write Linear Equations Answer Key
In lesson 6 homework practice, you will practice writing linear equations in point-slope form and slope-intercept form for different lines. You can check your answers using this answer key[^1^]. Remember to show your work and explain your reasoning.
#Slope-Intercept FormPoint-Slope Form
1.y = 3x + 21y - 6 = 3(x - (-5))
2.y = -4x + 9y - 9 = -4(x - (-5))
3.y = 2x + 1y - 1 9160f4acd4
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