Respuesta :
Answer:
The linear equation for the line which passes through the points given as (1,5) and (4,11), is written in the point-slope form as y=2x+3.
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (1,5) and (4,11).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 2
Determine the slope of the line.
The points through which the line passes are given as (1,5) and (4,11). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 11&5 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$4 \& 1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$\begin{aligned}m &=\frac{11-5}{4-1} \\m &=\frac{6}{3} \\m &=2\end{aligned}$[/tex]
Step 2 of 2
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
Substitute 2 for [tex]$m, 1$[/tex] for [tex]$x_{1}$[/tex], and 5 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,
[tex]$\begin{aligned}&y-5=2(x-1) \\&y-5=2 x-2 \\&y=2 x-2+5 \\&y=2 x+3\end{aligned}$[/tex]
This is the required linear equation.
