Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)
For lines to be parallel, they have to have the SAME slope.
For lines to be perpendicular, their slopes have to be the opposite/negative reciprocals (flipped sign and number)
For example:
slope is 2
perpendicular line's slope is -1/2
slope is -2/3
perpendicular line's slope is 3/2
9.) First find the slope of line PQ. Use the slope formula and plug in the two points.
P = (4, 1) (x₁ , y₁)
Q = (8, 4) (x₂ , y₂)
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{4-1}{8-4}[/tex]
[tex]m=\frac{3}{4}[/tex]
Line RS is parallel to line PQ, so they have the same slope of 3/4
[tex]y=\frac{3}{4}x+b[/tex]
To find "b", plug in the point R = (3, -2) into the equation
[tex]y=\frac{3}{4}x+b[/tex]
[tex]-2=\frac{3}{4}(3)+b[/tex]
[tex]-2=\frac{9}{4}+b[/tex] Subtract 9/4 on both sides
[tex]-2-\frac{9}{4}=b[/tex] Make the denominators the same
[tex]-\frac{8}{4} -\frac{9}{4}=b[/tex]
[tex]-\frac{17}{4}=b[/tex]
[tex]y = \frac{3}{4}x- \frac{17}{4}[/tex]
10.) Find the slope of line PQ
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{4-1}{8-4} =\frac{3}{4}[/tex]
Line RS is perpendicular to line PQ, so the slope of line RS is -4/3
y = -4/3x + b
Plug in the point R = (3, -2) into the equation to find "b"
y = -4/3x + b
-2 = -4/3(3) + b
-2 = -4 + b Add 4 on both sides
2 = b
[tex]y = -\frac{4}{3}x+2[/tex]
