Respuesta :
Answer:
The required linear equation satisfying the given points (2,4) and (4,10) is y=3x-2
Step-by-step explanation:
Two points are given in question, (2,4) and (4,10).
It is required to find out a linear equation satisfying the points (2,4) and (4,10).
To find it out, find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the
[tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]
Step 1 of 3
The slope of a line passing through the points (2,4) and (4,10) is given by
[tex]$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{10-4}{4-2} \\m &=\frac{6}{2} \\m &=3\end{aligned}$[/tex]
Step 2 of 3
Now use the slope m=3 and use one of the two given points and write the equation in point-slope form:
[tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$\\ $(y-4)=3(x-2)$[/tex]
Distribute 3 ,
[tex]$\begin{aligned}&y-4=3 x-3 \times 2 \\&y-4=3 x-6\end{aligned}$[/tex]
Step 3 of 3
This linear function can be written in the slope-intercept form by adding 4 on both sides,
[tex]$\begin{aligned}&y-4+4=3 x-6+4 \\&y=3 x-2\end{aligned}$[/tex]
So, this is the required linear equation.
