Question

Write the equation of the line given the following. Write the equation in slope-intercept form.
1) slope = 2/5 through the point (-1, -6)
2) Through the points (-2, 5) and (5, 8)
3) Through the points (-3, 7) and (5, 7)
4) Through the points (6, 1) and (6, -5)
Thank you so much for your help in advance!

Answer 1

Just to get formulas out the way so that I don't have to write them out every time:

slope-intercept form: y = mx + b
where m is the slope and b is the y-intercept.

slope = $\frac{Y2-Y1}{X2-X1}$
where X1 and Y1 are the x- and y-coordinates in the first ordered pair. Same applies for X2 and Y2.

1) They give you the slope so plug it in along with the point given and solve for b. 

y = 2/5x + b
- 6 = 2/5(- 1) + b
- 6 = - 2/5 + b
- 6 + 2/5 = b
- 30/5 + 2/5 = b
- 28/5 = b

Your equation: y = - 2/5x - 28/5

2) Find your slope first then plug in any point to solve for b.
m = $\frac{8 - 5}{5 - (- 2)} = \frac{3}{7}$

y = 3/7x + b
5 = 3/7(- 2) + b
5 = - 6/7 + b
5 + 6/7 = b
35/7 + 6/7 = b
41/7 = b

y = 3/7x + 41/7

3) Same thing as above. 
m = $\frac{7 - 7}{5 - (- 3)} = \frac{0}{8} = 0$

y = 0x + b
y = b
7 = b

y = 7

4) Same as above
m = $\frac{- 5- 1}{6-6} = \frac{- 6}{0} =$ undefined. 

Because your slope is undefined, it is no longer a "y =" problem but rather an "x =" equation. You then take the x-values of the two ordered pairs (they should match) and that becomes the right side of the equal sign.

x = 6