Question

Stuck Please help...... 1,2,5,6

Answer 1

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

$y=-\frac{7}{5}x+b$    Plug in (2, -3) to find "b"

$-3 = -\frac{7}{5}(2)+b$

$-3=-\frac{14}{5}+b$       Add 14/5 on both sides

$-3+\frac{14}{5}=b$     Make the denominators the same

$\frac{-15}{5}+\frac{14}{5} =b\\-\frac{1}{5}=b$

$y=-\frac{7}{5}x-\frac{1}{5}$

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 = $\frac{1}{2}$(4) + b

5 = 2 + b

3 = b

$y=\frac{1}{2} x+3$

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

$y=-\frac{2}{5}x-6$

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

$y=\frac{5}{2}x+\frac{19}{2}$