Question

Line "m" has intercepts (7,0) and (0, -2)

What is the equation of line "m"?

Is the point (49, -16) also on line "m"? How do you know?

Answer 1

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.


`slope = (y_2-y_1)/(x_2-x_1) = (-2-0)/(0-7) = (-2)/(-7) = \boxed{(2)/(7)=m}`

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)!


`y-intercept=\boxed{-2=b}`

Now we just need to put our slope and y-intercept into the equation.


`\boxed{\boxed{y=(2)/(7)x-2}}`

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!


`-16 = (2)/(7)*49-2 \\ -16 = 14 - 2 \\ -16 \\eq 12,\ \therefore line\ m\ does\ not\ contain\ (49, -16)`