We are already given the slope (3) so we can set that for m.
y = 3x + b
Now all we need is the y-intercept. Using the slope and the ordered pair (3,1), we can calculate at what number the line will cross directly on the y-axis. For the line to cross directly on top of the y axis, the x-value must be 0. When the x equals 0, whatever the y equals is our y-intercept.
Currently the x value is 3. We need to find a way to turn the 0. Use the slope formula ( [tex] \frac{rise}{run} [/tex] = 3; [tex] \frac{3}{1} [/tex] Note: that x equals [tex] \frac{x}{1} [/tex] ) and reverse it to [tex] \frac{(-)3}{(-)1} [/tex]. Note that the rise deals with the y-value whilst the run deals with the x-value. If it's positive that means +. If it's negative that means -. We turned the slope negative so we could do inverse operations. This let's us find out what the y-value would equal if x was 0.
(3,1) -> (3 - 1, 1 - 3) -> (2, -2) -> (2 - 1, -2 - 3) -> (1,-5) -> (1 - 1, -5 - 3) -> (0,-8).
When x was 0, y was -8. Therefore the y-intercept is -8.
Equation: y = 3x - 8.
View the attachment to see it graphed.
