Question

Which equation is perpendicular to y = 4x - 6 and passes through point (8, 12).

Answer 1

Answer:

The line is ;

4y = -x + 56

or

y = -x/4 + 14

Step-by-step explanation:

Generally, the equation of a straight line is;

y = mx + c

where m represents the slope

so for y = 4x - 6

The slope is 4

If two lines are perpendicular, the product of their slopes is -1

So for the second line, the slope will be -1/4

The equation in the point slope format will be ;

y-12 = -1/4(x-8)

y-12 = -x/4 + 2

Multiply through by 4

4y-48 = -x + 8

4y = -x + 8 + 48

4y = - x + 56

Answer 2

The equation of the line that passes through (8, 12) and is perpendicular to y = 4x - 6 is:

$y - 12 = -\frac{1}{4} (x - 8)$ (point-slope form)

or

$y = -\frac{1}{4}x + 14$ (slope-intercept form)

Recall:

• Point-slope equation is given in the form of: y - b = m(x - a)

• Slope-intercept equation is given in the form of: y == mx + b

• Where, m is the slope

• The slopes of two lines that are perpendicular to each other are the negative reciprocal of one another.

Given:

y = 4x - 6

• Slope (m) = 4

• The negative reciprocal of 4 is: -1/4

To write the equation of a line that passes through (8, 12) and is also perpendicular to y = 4x - 6, substitute m = -1/4 and (8, 12) into

y - b = m(x - a)

• Thus:

$y - 12 = -\frac{1}{4} (x - 8)$ (point-slope form)

Rewrite in slope-intercept form

$y - 12 = -\frac{1}{4} (x - 8)\\\\y - 12 = -\frac{1}{4}x + 2\\\\y = -\frac{1}{4}x + 2 + 12\\\\y = -\frac{1}{4}x + 14$(point-slope form)

Therefore, the equation of the line that passes through (8, 12) and is perpendicular to y = 4x - 6 is:

$y - 12 = -\frac{1}{4} (x - 8)$ (point-slope form)

or

$y = -\frac{1}{4}x + 14$ (slope-intercept form)

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