Question

In Exercises 17-24, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.) $$ \begin{array}{ll} \text { Point } & \text { Slope } \\ (-1,-6) & m=\frac{1}{2} \end{array} $$

Name: Problem 24, Chapter 1: Precalculus with Limits: A Graphing Approach
Uploaded: 2021-06-11T10:41:48-08:00
Duration: 2 min 27 s
Channel: Dwijendra Rao
Description: In Exercises 17-24, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.) Point Slope (-1,-6) m=(1)/(2)

   In Exercises 17-24, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
$$
\begin{array}{ll}
\text { Point } & \text { Slope } \\
(-1,-6) & m=\frac{1}{2}
\end{array}
$$

Precalculus with Limits: A Graphing Approach

Ron Larson 6th Edition

Chapter 1, Problem 24

Instant Answer

Solved by Expert Dwijendra Rao

06/11/2021

Step 1

We are given a point $(-1, -6)$ and the slope $m = \frac{1}{2}$ of the line. The slope of a line indicates the change in the y-coordinate relative to the change in the x-coordinate between any two points on the line. Show more…

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In Exercises 17-24, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.) $$ \begin{array}{ll} \text { Point } & \text { Slope } \\ (-1,-6) & m=\frac{1}{2} \end{array} $$

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Key Concepts

Finding Additional Points on a Line

Once a line’s equation is determined using the point-slope form, additional points can be found by selecting various x-values and substituting them into the equation to solve for the corresponding y-values. This systematic approach leverages the constant slope to identify other positions that lie on the same straight line.

Slope

Slope represents the steepness or incline of a line and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It indicates how much the y-coordinate changes for a unit increase in the x-coordinate.

Point-Slope Form

The point-slope form is a way to express the equation of a line given a known point on the line and its slope. This form, written as y - y? = m(x - x?), serves as a flexible tool to quickly create the line’s equation using the relationship between the point's coordinates (x?, y?) and the slope m.

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