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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 3: Q.460 (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 $y = \frac{3}{4} x - 2$ .

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 $(0, - 2), (4, 1)$ .

The slope between two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Find the slope.

$m = \frac{1 - (- 2)}{4 - 0} m = \frac{3}{4}$

Substitute $m = \frac{3}{4}, x_{1} = 0, y_{1} = - 2$ in $y - y_{1} = m (x - x_{1})$ .

$\begin{array}{rcl} y - (- 2) & = & \frac{3}{4} (x - 0) \\ y + 2 & = & \frac{3}{4} x \\ y & = & \frac{3}{4} x - 2 \end{array}$

The line equation is $y = \frac{3}{4} x - 2$ .

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Most popular questions from this chapter

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

$f (x) = x^{3} - 2$

Graph the equations $y = - \frac{1}{3} x, y = - \frac{1}{3}$ in the same cartesian plane.

Find the equation of the line shown in each graph and write the equation in slope-intercept form.

Find the intercepts of the graph

.

Use graph of $y = 3 x - 1$ . For each ordered pair, decide :

(a) Is the ordered pair $A (0, - 1), B (2, 5)$ a solution to the equation.

(b) Is the point $A (0, - 1), B (2, 5)$ on the line?

See all solutions

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