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

`(y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1))`

This can be written as,

`y-y_(1)=\left((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((10-(-2))/(3-(-1))\right)(x-(-1))} \\\\ {\Rightarrow y+2=(10+2)/(3+1)(x+1)} \\\\ {\Rightarrow y+2=(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`