Question

write an equation in slope intercept form of a line that passes through the point (14,8) and is (a) parallel (b) perpendicular to the line that passes through the points (4,9) and (-3,6)

Answer 1

Slope-intercept form:

y = mx + b       "m" is the slope, "b" is the y-intercept (the y value when x = 0)

First find the slope of the line that passes through (4,9) and (-3,6).

Use the slope formula and plug in the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{6-9}{-3-4}$

$m=\frac{-3}{-7} =\frac{3}{7}$

A.) For lines to be parallel, their slopes have to be the same.

Since the given line's slope is 3/7, the parallel line's slope is also 3/7

y = 3/7x + b    To find "b", plug in the point (14,8) into the equation

8 = 3/7(14) + b

8 = 42/7 + b

8 = 6 + b    Subtract 6 on both sides

2 = b

$y=\frac{3}{7}x+2$

B.) For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 3

perpendicular line's slope is -1/3

slope is -2/3

perpendicular line's slope is 3/2

Since the given line's slope is 3/7, the perpendicular line's slope is -7/3

y = -7/3x + b    Plug in (14, 8) to find "b"

8 = -7/3(14) + b

8 = -98/3 + b   Add 98/3 on both sides

8 + 98/3 = b       Make the denominators the same

24/3 + 98/3 = b

122/3 = b

$y=-\frac{7}{3}x+\frac{122}{3}$