Find an equation for the line containing the points P = (4, 2) and Q = (- 6, 10). Write the equation using the slope–intercept form.

First, find the gradient, given by m,

m=\frac{y_2-y_1}{x_2-x_1}

Then, use the equation formula,

\frac{y-y_o}{x-x_o}=m

Where y_o and x_o are points that you already have, that is you use (4, 2) or (-6, 10), then cross multiply. Make y the subject of formula, and you're done! :)

The slope-intercept form of a line is an equation for that line in this form

Y=mX + b

where m is the slope of the line and b is the intercept.

You have two points, (4,2) and (-6,10). You can draw a line between them. The slope of the line is

Slope = \frac {\Delta\,Y}{\Delta\,X} = \frac {(10-2)}{(-6-4)} = -\frac {8}{10} = -0.8

Now you have the slope. The line becomes

Y=-0.8X + b

To solve for b (the y-intercept), simply take one of your points and plug it into the equation say, (X,Y) = (4,2). Check by inserting the second point.