Question

How do you do this?
Write the equation of a line in slope intercept form that passes through (2, 4) and (5, 4).

Answer 1

first find the slope, m: \(\huge m=\frac{y_2-y_1}{x_2-x_1} \)
then put in point-slope for: \(\huge y-y_1=m(x-x_1) \)
then solve for y to get in slope-intercept form: \(\huge y=mx+b \)

Answer 2

First off what is the slope? Rise over run, right? It'll be rising and running the same amount between every point on the line! So you can just take the difference in rise over the difference in run to get the slope. So literally this equation shows this:
\[(y _{2}-y_{1})/(x _{2}-x_{1})=m\]
now that you have your m in y=mx+b what you can simply do is take an ordered pair, either one, it doesn't matter which! and plug it into your equation since you now know m, x, and y to solve for b!