Question

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

36. x-intercept at (-2, 0) and y-intercept at (0, -3)

Answer 1

The linear equation for the line with an x - intercept at (-2,0) and y-intercept at (0,-3) is found as
`$y=-(3)/(2) x-3$`.

Explanation:

A condition is given that a line has an x- intercept at (-2,0) and y - intercept at (0,-3).

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

Step 1 of 2

Determine the slope of the line.

The points of the intercepts of the line are given as (-2,0) and (0,-3). Next, the formula for the slope is given as,

`m=(y_(2)-y_(1))/(x_(2)-x_(1))$`

Substitute -3&0 for
`$y_(2)$` and
`$y_(1)$` respectively, and 0&-2 for
`$x_(2)$` and
`$x_(1)$` respectively in the above formula. Then simplify to get the slope as follows,

`$$\begin{aligned}m &=(-3-0)/(0-(-2)) \\m &=(-3)/(2) \\m &=-(3)/(2)\end{aligned}$$`

Step 2 of 2

Write the equation in the slope-intercept form.

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

y=mx+b

The coordinates at the y- intercept is (0,-3). Now, as the y- coordinate is -3, so b=-3.

So, substitute -3 for b and
`$-(3)/(2)$` for m in the equation y=mx+b, and simplify to get the equation as follows,

`$$\begin{aligned}&y=-(3)/(2) x+(-3) \\&y=-(3)/(2) x-3\end{aligned}$$`

This is the required linear equation.