Respuesta :
Answer:
The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].
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,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$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{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
[tex]$y=m x+b$[/tex]
The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.
So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,
[tex]$y=\frac{4}{5} x+4$[/tex]
This is the required linear equation.
