## 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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