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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 3: Q.461 (page 357)

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.

Short Answer

Expert verified

The slope-intercept form of the equation of the line in the shown graph is $y = - 4 or y = 0 x - 4$ .

Step by step solution

01

Step 1. Given information:

The provided graph of a line equation is:

02

Step 2. Evaluate/formulas

From the graph, take two points that lie on the line are say $(4, - 4), (0, - 4)$ .

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

03

Step 3. Find the equation of the line.

Here, $(x_{1}, y_{1}) = (0, - 4), (x_{2}, y_{2}) = (4, - 4)$ .

Find slope.

$\begin{array}{rcl} m & = & \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ = & \frac{- 4 - (- 4)}{4 - 0} \\ = & \frac{0}{4} \\ = & 0 \end{array}$

Substitute $m = 0, x_{1} = 0, y_{1} = - 4$ in $y - y_{1} = m (x - x_{1})$ .

$\begin{array}{rcl} y - (- 4) & = & 0 (x - 0) \\ y + 4 & = & 0 \\ y & = & - 4 \end{array}$

The line equation is $y = - 4$ .

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Most popular questions from this chapter

Determine whether each graph is the graph of a function.

Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.
$(- 2, 1), (- 3, - 1), (4, - 4), (- 4, 4), (- 4, \frac{3}{2})$

Graph: f(x) = 3

In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.

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