The equation for the linear function whose graph contains the points (-1, -2) and (3, 10) is y = 3x + 1
<h3><u>Solution:</u></h3>
Given that linear function whose graph contains the points (-1, -2) and (3, 10)
We have to find the equation of line
Any function of the form f (x) = m x + b, where m is not equal to 0 is called a linear function
So let us use the slope intercept form
<em><u>The slope intercept form is given as:</u></em>
y = mx + c
Where "m" is the slope of line and "c" is the y - intercept
Let us first find slope of line containing points (-1, -2) and (3, 10)
<em><u>The slope of line is given as:</u></em>
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![\text {Here } x_{1}=-1 \text { and } y_{1}=-2 \text { and } x_{2}=3 \text { and } y_{2}=10](https://tex.z-dn.net/?f=%5Ctext%20%7BHere%20%7D%20x_%7B1%7D%3D-1%20%5Ctext%20%7B%20and%20%7D%20y_%7B1%7D%3D-2%20%5Ctext%20%7B%20and%20%7D%20x_%7B2%7D%3D3%20%5Ctext%20%7B%20and%20%7D%20y_%7B2%7D%3D10)
![m=\frac{10-(-2)}{3-(-1)}=\frac{12}{4}=3](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B10-%28-2%29%7D%7B3-%28-1%29%7D%3D%5Cfrac%7B12%7D%7B4%7D%3D3)
Thus the slope of line is "m" = 3
Substitute m = 3 and (x, y) = (-1, -2) in y = mx + c
-2 = 3(-1) + c
-2 = -3 + c
c = -2 + 3 = 1
Now substitute c = 1 and m = 3 in slope intercept form to get equation of line
y = 3x + 1
Thus the equation for the linear function is found out