Question

Find the equation of the line passing through the points (10,8) and (-10,30). Write your answer in the form

Answer 1

The equation of a line in slope-intercept form is given by:

$y=mx+b$

Where m is the slope and b is the y-intercept.

We know two points on the line: (10,8) and (-10,30).

The slope can be found by using the following formula:

$m=\frac{y2-y1}{x2-x1}$

Where (x1,y1) and (x2,y2) are the coordinates of two points on the line. By replacing the known coordinates we obtain:

$m=\frac{30-8}{-10-10}=\frac{22}{-20}=-\frac{11}{10}$

The y-intercept can be found by replacing the slope and one of the points in the slope-intercept formula, and solving for b:

$\begin{gathered} 8=-\frac{11}{10}\cdot10+b \\ 8=-11+b \\ 8+11=b \\ b=19 \end{gathered}$

Thus, the equation of the line is:

$y=-\frac{11}{10}x+19$