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)

Equation in slope intercept form (parallel line)

Equation of perpendicular line in slope intercept form is

Given :

an equation in slope intercept form of a line that passes through the point (14,8)

Two given points are (4,9) and (-3,6)

Lets find out the slope of the given two points

Slope of parallel lines are same. So we use the above slope to find the equation of parallel line

The line passes through the point (14,8)

Equation of line is

y-y1=m(x-x1)

use the slope m= 3/7 and point (14,8)

Slope of perpendicular lines are negative reciprocal of one another

Slope of perpendicular line is

Now we find equation of line that passes through the point (14,8) and slope -7/3

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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:

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

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

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