Chapter 4: Q. 293 (page 520)

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y = m x + b$ .
$y = - \frac{2}{5} x + 3$

Short Answer

Expert verified

The slope of the line is $m = - \frac{2}{5}$ and the y-intercept is $(0, 3)$ .

Step by step solution

Step 1. Given information.

The given graph is:

The given equation is $y = - \frac{2}{5} x + 3$ .

Step 2. Determine the slope and y-intercept from the graph.

Select any two points on the line. We'll use the points $(0, 3)$ and $(5, 1)$ . Here, rise is $1 - 3 = - 2$ and run is $5 - 0 = 5$ .

$\begin{array}{rcl} m & = & \frac{Rise}{Run} \\ = & \frac{- 2}{5} \\ = & - \frac{2}{5} \end{array}$

The graph crosses the y-axis at $(0, 3)$ , so the y-intercept of the graph is $(0, 3)$ .

Step 3. Determine the slope and y-intercept from the equation.

On comparing $y = - \frac{2}{5} x + 3$ and $y = m x + b$ ,

$\begin{array}{rcl} m & = & - \frac{2}{5} \\ b & = & 3 \end{array}$

The slope is the same as the coefficient of x and the y-coordinate of the y-intercept is the same as the constant term.

Step 4. Conclusion.

The slope of the line is $m = - \frac{2}{5}$ and the y-intercept is $(0, 3)$ .

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In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y = m x + b$ .
$y = - \frac{2}{5} x + 3$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the slope and y-intercept from the graph.

Step 3. Determine the slope and y-intercept from the equation.

Step 4. Conclusion.

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In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation y=mx+b.y=-25x+3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the slope and y-intercept from the graph.

Step 3. Determine the slope and y-intercept from the equation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y = m x + b$ .
$y = - \frac{2}{5} x + 3$