Chapter 4: Q. 290 (page 519)

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y = m x + b$ .
$y = - x + 4$

Short Answer

Expert verified

The slope of the line is $m = - 1$ and the y-intercept is $(0, 4)$ .

Step by step solution

Step 1. Given information.

The given graph is:

The given equation is $y = - x + 4$ .

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

Select any two points on the line. We'll use the points $(0, 4)$ and $(4, 0)$ . Here, rise is $0 - 4 = - 4$ and run is $4 - 0 = 4$ .

$\begin{array}{rcl} m & = & \frac{Rise}{Run} \\ = & \frac{- 4}{4} \\ = & - 1 \end{array}$

The graph crosses the y-axis at $(0, 4)$ , so the y-intercept of the graph is $(0, 4)$ .

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

On comparing $y = - x + 4$ and $y = m x + b$ ,

$\begin{array}{rcl} m & = & - 1 \\ b & = & 4 \end{array}$

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 $m = - 1$ and the y-intercept is $(0, 4)$ .

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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 $y = m x + b$ .
$y = - x + 4$

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=-x+4

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

Calculus

Geometry

Logic and Functions

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

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 $y = m x + b$ .
$y = - x + 4$