Question

What is an equation for the linear function whose graph contains the points (−1, −2) and (3, 10)

Answer 1

The linear function is (4, 12)

Answer 2

The line equation that passes through the given points is $3x-y + 1 = 0$

SOLUTION:

Given, two points are A(-1, -2) and B(3, 10).

We need to find the line equation that passes through the given two points.  We know that, general equation of a line passing through two points $(x_1, y_1), (x_2, y_2)$ is given by

$\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

This can be written as,

$y-y_{1}=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\left(x-x_{1}\right) \rightarrow(1)$

here, in our problem $x_1 = - 1;  y_1 = - 2;  x_2 = 3 \text { and } y_2 = 10.$

Now substitute the values in (1)

$\begin{array}{l}{y-(-2)=\left(\frac{10-(-2)}{3-(-1)}\right)(x-(-1))} \\\\ {\Rightarrow y+2=\frac{10+2}{3+1}(x+1)} \\\\ {\Rightarrow y+2=\frac{12}{4}(x+1)} \\\\ {\Rightarrow y+2=3(x+1)} \\\\ {\Rightarrow y+2=3 x+3} \\\\ {\Rightarrow 3 x-y+3-2=0} \\\\ {\Rightarrow 3 x-y+1=0}\end{array}$

Hence, the line equation that passes through the given points is $3x-y + 1 = 0$