The equation for the linear function whose graph contains the points (-1, -2) and (3, 10) is y = 3x + 1
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
The slope intercept form is given as:
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)
The slope of line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text {Here } x_{1}=-1 \text { and } y_{1}=-2 \text { and } x_{2}=3 \text { and } y_{2}=10[/tex]
[tex]m=\frac{10-(-2)}{3-(-1)}=\frac{12}{4}=3[/tex]
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
