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Math  /  Algebra

Questionhe equation of line cc is y=18x+10y=\frac{1}{8} x+10. Line dd is perpendicular to line cc and passes through −1,1)-1,1). What is the equation of line dd ? rite the equation in slope-intercept form. Write the numbers in the equation as simplified oper fractions, improper fractions, or integers.

Studdy Solution

STEP 1

1. Line c c has the equation y=18x+10 y = \frac{1}{8}x + 10 .
2. Line d d is perpendicular to line c c .
3. Line d d passes through the point (−1,1)(-1, 1).
4. We need to find the equation of line d d in slope-intercept form, y=mx+b y = mx + b .

STEP 2

1. Determine the slope of line d d .
2. Use the point-slope form to find the equation of line d d .
3. Convert the equation to slope-intercept form.

STEP 3

The slope of line c c is 18 \frac{1}{8} .
For line d d to be perpendicular to line c c , its slope must be the negative reciprocal of 18 \frac{1}{8} .
Calculate the negative reciprocal:
md=−118=−8 m_d = -\frac{1}{\frac{1}{8}} = -8

STEP 4

Use the point-slope form of a line equation, which is y−y1=m(x−x1) y - y_1 = m(x - x_1) , where m m is the slope and (x1,y1)(x_1, y_1) is a point on the line.
Substitute m=−8 m = -8 and the point (−1,1)(-1, 1):
y−1=−8(x+1) y - 1 = -8(x + 1)

STEP 5

Simplify the equation:
y−1=−8x−8 y - 1 = -8x - 8

STEP 6

Convert the equation to slope-intercept form y=mx+b y = mx + b .
Add 1 to both sides:
y=−8x−8+1 y = -8x - 8 + 1
y=−8x−7 y = -8x - 7
The equation of line d d in slope-intercept form is:
y=−8x−7 y = -8x - 7

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