Question

A line contains the point (8, 5). if the slope of the line is 5/7, write the equation of the line using point-slope form.

Answer 1

First of all, you organize all of the info that you're given. We know that the points are (x, y). Therefore, 8 is x and 5 is y. 5/7 is your m, since m represents the slope. 

x = 8
y = 5
m = 5/7
b = y-intercept, which is the missing info

Then, you put it into a multi-step equation.

The slope equation formula is y = mx + b. Now, we solve for the equation.

y = mx + b

5 = 5/7(8) + b (missing info is the y-intercept, so that's why it stays as "b")

5 = 5/7(8/1) + b (any whole number converted into fractions always have a denominator of 1)

       5 = 40/7 + b        At this point, since 5 as a fraction is 5/1, you need to 
-40/7   -40/7 + b        multiply the numerator and denominator by 7 so that 
_____________      you're able to subtract 40/7 from it. So, 5 x 7 = 35 and 
                                   1 x 7 = 7, giving you the fraction of 35/7. 35/7 - 40/7 =
                                   -5/7.
-5/7 = b

Finally, you've got all the info you need to write the equation. As a result, you just substitute the letters with the numbers:

m = 5/7
b = -5/7

y = 5/7x - 5/7 
I hope I helped and that you understood my explanations! :)