The equation of a line is usually written in what's called slope-intercept form.
Slope-intercept form is written as y = mx + b where m = slope and b = the y-intercept.
The slope of a line can easily be found just by using two points on the line. The slope is equal to the rise over the run, or the difference in y over the difference in x, between the two points.
[tex]slope = \frac{y_2-y_1}{x_2-x_1} = \frac{-2-0}{0-7} = \frac{-2}{-7} = \boxed{\frac{2}{7}=m}[/tex]
The y-intercept of the line is the point at which it intersects the y-axis. (The vertical axis.) All points on the y-axis have an x coordinate of 0, so we would then add or subtract the rise and run to a point on the line until we reached x = 0.
Fortunately, we already have this point! It's (0, -2)!
[tex]y-intercept=\boxed{-2=b}[/tex]
Now we just need to put our slope and y-intercept into the equation.
[tex]\boxed{\boxed{y=\frac{2}{7}x-2}}[/tex]
And to test if a point is on this line, just plug in the x and y coordinates and see if the equation is true!
[tex]-16 = \frac{2}{7}*49-2 \\ -16 = 14 - 2 \\ -16 \neq 12,\ \therefore line\ m\ does\ not\ contain\ (49, -16)[/tex]
