Question

37. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

Answer 1

Answer:

The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as $y=\frac{4}{5} x+4$.

Step-by-step explanation:

A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).

It is asked to find a linear equation satisfying the given condition.

To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.

Step 1 of 2

Determine the slope of the line.

The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 4&0 for $y_{2}$ and $y_{1}$respectively, and 0&-5 for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,

$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$

Step 2 of 2

Write the equation in the slope-intercept form.

The slope-intercept form of a line is given as follows,

$y=m x+b$

The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.

So, substitute 4 for b and $\frac{4}{5}$ for m in the equation y=mx+b, as follows,

$y=\frac{4}{5} x+4$

This is the required linear equation.