Respuesta :
Answer:
The linear equation for the line with an x - intercept at (-2,0) and y-intercept at (0,-3) is found as [tex]$y=-\frac{3}{2} x-3$[/tex].
Step-by-step 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,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute -3&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 0&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$\begin{aligned}m &=\frac{-3-0}{0-(-2)} \\m &=\frac{-3}{2} \\m &=-\frac{3}{2}\end{aligned}$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
y=mx+b
The coordinates at the y- intercept is (0,-3). Now, as the y- coordinate is -3, so b=-3.
So, substitute -3 for b and [tex]$-\frac{3}{2}$[/tex] for m in the equation y=mx+b, and simplify to get the equation as follows,
[tex]$\begin{aligned}&y=-\frac{3}{2} x+(-3) \\&y=-\frac{3}{2} x-3\end{aligned}$[/tex]
This is the required linear equation.
