Question

What is an equation for the linear function whose graph contains the points (-1,-2) and (3,10) enter your answers in the boxes

Answer 1

The equation for the linear function whose graph contains the points (-1, -2) and (3, 10) is y = 3x + 1

Solution:

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:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=-1 \text { and } y_{1}=-2 \text { and } x_{2}=3 \text { and } y_{2}=10$

$m=\frac{10-(-2)}{3-(-1)}=\frac{12}{4}=3$

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