Question

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope $=-4,$ passing through $(-5,-2)$

Name: Problem 6, Chapter 3: Introductory Algebra for College Students
Uploaded: 2021-02-11T05:36:29-08:00
Duration: 2 min 43 s
Channel: Anas Venkitta
Description: Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope =-4, passing through (-5,-2)

   Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope $=-4,$ passing through $(-5,-2)$

Introductory Algebra for College Students

Robert Blitzer 6th Edition

Chapter 3, Problem 6

Instant Answer

Solved by Expert Anas Venkitta

02/11/2021

Step 1

We can use the point-slope form of the line which is given by $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is the point through which the line passes. Substituting the given values, we get $y - (-2) = -4(x - (-5))$. Show more…

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Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope $=-4,$ passing through $(-5,-2)$

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Key Concepts

Point-Slope Form

The point-slope form of a linear equation, given as y - y1 = m(x - x1), is used to develop the equation of a line when a point (x1, y1) on the line and the slope m are known. It provides a direct way to write the equation without first finding the y-intercept.

Slope-Intercept Form

The slope-intercept form, written as y = mx + b, displays both the slope m and the y-intercept b of a line. It is a widely used representation for linear equations and is particularly useful for graphing a line, as it clearly shows where the line crosses the y-axis.

Conversion Between Forms

Converting a linear equation from point-slope form to slope-intercept form involves algebraically manipulating the equation to solve for y. This process typically involves distributing the slope and isolating y to clearly identify the y-intercept, thus facilitating graphing and further analysis.

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