Chapter 3: Q 463R (page 357)

In the following exercises, find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.
slope $m = \frac{3}{5}$ , point $(10, 6)$ .

Short Answer

Expert verified

The slope-intercept form of the line equation with the slope $m = \frac{3}{5}$ and passes through the point $(10, 6)$ is $y = \frac{3}{5} x$ .

Step by step solution

Given information

The slope is $m = \frac{3}{5}$ and the point is $(10, 6)$ .

Definitions

The point-slope form of a line equation that passes through the point $(x_{1}, y_{1})$ with slope $m$ is $y - y_{1} = m (x - x_{1})$ .

The slope-intercept form of the line equation is $y = m x + b$ .

Simplify

Here, $(x_{1}, y_{1}) = (10, 6), m = \frac{3}{5}$ .

Substitute these values in $y - y_{1} = m (x - x_{1})$ .

$\begin{array}{rcl} y - 6 & = & \frac{3}{5} (x - 10) \\ y - 6 & = & \frac{3}{5} x - \frac{3}{5} \cdot 10 \\ y - 6 & = & \frac{3}{5} x - 6 \\ y & = & \frac{3}{5} x \end{array}$

The line equation is $y = \begin{array}{rcl} \frac{3}{5} \end{array} \begin{array}{rcl} x \end{array}$ .

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In the following exercises, find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.
slope $m = \frac{3}{5}$ , point $(10, 6)$ .

Short Answer

Step by step solution

Given information

Definitions

Simplify

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In the following exercises, find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.slope m=35, point10,6.

Short Answer

Step by step solution

Given information

Definitions

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Applied Mathematics

Statistics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.
slope $m = \frac{3}{5}$ , point $(10, 6)$ .