Respuesta :
Answer:
The equation of the line that passes through the points (2a, b) and (a, b+1) is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
Step-by-step explanation:
The given points are (2a, b) and (a, b+1).
It is required to find the equation of the line that passes through the points. the slope-intercept form.
Step 1 of 4
Using the given two points, to find the slope.
Given points are (2a, b) and (a, b+1).
Substitute [tex]$x_{1}[/tex]=2a,
[tex]$\begin{aligned}&y_{1}=b \\&x_{2}=a \text { and } \\&y_{2}=b+1\end{aligned}$[/tex]
into the formula, [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Step 2 of 4
Simplify [tex]$m=\frac{b+1-b}{a-2 a}$[/tex], further
[tex]$\begin{aligned}m &=\frac{b+1-b}{a-2 a} \\m &=-\frac{1}{a}\end{aligned}$[/tex]
As a result, the slope is [tex]$m=-\frac{1}{a}$[/tex].
Step 3 of 4
Use the slope [tex]$m=-\frac{1}{a}$[/tex] and the coordinates of one of the points (2a, b) into the point-slope form, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex].
Substitute [tex]$m=-\frac{1}{a}$[/tex],
[tex]x_{1}=2 a$ and$y_{1}=b$[/tex]
into the formula, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$y-b=-\frac{1}{a}(x-2 a)$[/tex]
[tex]$y-b=-\frac{1}{a} x+2$[/tex]
Step 4 of 4
Rewrite the above equation as a slope-intercept equation. So, from the above term [tex]$y-b=-\frac{1}{a} x+2$[/tex], Add b on each side.
[tex]$\begin{aligned}&y-b=-\frac{1}{a} x+2 \\&y=-\frac{1}{a} x+2+b\end{aligned}$[/tex]
Therefore, the equation of the line that passes through the points is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
