Slope-intercept form:
y = mx + b "m" is the slope, "b" is the y-intercept
For lines to be parallel, they have to have the SAME slope.
1.) The given line's slope is -7/5, so the parallel line's slope is also -7/5
[tex]y=-\frac{7}{5}x+b[/tex] Plug in (2, -3) to find "b"
[tex]-3 = -\frac{7}{5}(2)+b[/tex]
[tex]-3=-\frac{14}{5}+b[/tex] Add 14/5 on both sides
[tex]-3+\frac{14}{5}=b[/tex] Make the denominators the same
[tex]\frac{-15}{5}+\frac{14}{5} =b\\-\frac{1}{5}=b[/tex]
[tex]y=-\frac{7}{5}x-\frac{1}{5}[/tex]
2.) The given line's slope is 1/2, so the parallel line's slope is also 1/2
y = 1/2x + b Plug in (4,5) to find "b"
5 = [tex]\frac{1}{2}[/tex](4) + b
5 = 2 + b
3 = b
[tex]y=\frac{1}{2} x+3[/tex]
5.) The given line's slope is -2/5, so the parallel line's slope is also -2/5
y = -2/5x + b Plug in (-5, -4)
-4 = -2/5(-5) + b
-4 = 2 + b
-6 = b
[tex]y=-\frac{2}{5}x-6[/tex]
6.) -5x + 2y = 6 Isolate "y", add 5x on both sides
2y = 6 + 5x Divide 2 on both sides
y = 3 + 5/2x
The slope is 5/2, so the parallel line's slope is also 5/2
y = 5/2x + b Plug in (-3,2)
2 = 5/2(-3) + b
2 = -15/2 + b Add 15/2 on both sides
2 + 15/2 = b Make the denominator the same
4/2 + 15/2 = b
19/2 = b
[tex]y=\frac{5}{2}x+\frac{19}{2}[/tex]
