Line s has an equation of y=8x+7. Line t is perpendicular to line s and passes through (−8,−2). What is the equation of line t?Write the equation in slope-intercept form.
Q. Line s has an equation of y=8x+7. Line t is perpendicular to line s and passes through (−8,−2). What is the equation of line t?Write the equation in slope-intercept form.
Determine slope of line s: Determine the slope of line s. The equation of line s is given by y=8x+7. The slope-intercept form of a line is y=mx+b, where m is the slope and b is the y-intercept. Comparing the given equation with the slope-intercept form, we find that the slope (m) of line s is 8.
Find slope of line t: Find the slope of line t.Since line t is perpendicular to line s, its slope will be the negative reciprocal of the slope of line s. The negative reciprocal of 8 is −81.
Use point-slope form: Use the point-slope form to find the equation of line t. The point-slope form of a line is y−y1=m(x−x1), where m is the slope and (x1,y1) is a point on the line. We know that line t passes through the point (−8,−2) and has a slope of −81. Plugging these values into the point-slope form, we get: y−(−2)=−81(x−(−8))
Simplify equation of line t: Simplify the equation of line t.Now we simplify the equation from the previous step:y+2=−81(x+8)y+2=−81x−1Subtract 2 from both sides to get the equation in slope-intercept form:y=−81x−1−2y=−81x−3
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