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Line ss has an equation of y=8x+7y = 8x + 7. Line tt is perpendicular to line ss and passes through (8,2)(-8,-2). What is the equation of line tt?\newlineWrite the equation in slope-intercept form.

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Q. Line ss has an equation of y=8x+7y = 8x + 7. Line tt is perpendicular to line ss and passes through (8,2)(-8,-2). What is the equation of line tt?\newlineWrite the equation in slope-intercept form.
  1. Determine slope of line ss: Determine the slope of line ss. The equation of line ss is given by y=8x+7y = 8x + 7. The slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Comparing the given equation with the slope-intercept form, we find that the slope (mm) of line ss is 88.
  2. Find slope of line t: Find the slope of line t.\newlineSince line t is perpendicular to line s, its slope will be the negative reciprocal of the slope of line s. The negative reciprocal of 88 is 18-\frac{1}{8}.
  3. Use point-slope form: Use the point-slope form to find the equation of line tt. The point-slope form of a line is yy1=m(xx1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line. We know that line tt passes through the point (8,2)(-8, -2) and has a slope of 18-\frac{1}{8}. Plugging these values into the point-slope form, we get: y(2)=18(x(8))y - (-2) = -\frac{1}{8}(x - (-8))
  4. Simplify equation of line t: Simplify the equation of line t.\newlineNow we simplify the equation from the previous step:\newliney+2=18(x+8)y + 2 = -\frac{1}{8}(x + 8)\newliney+2=18x1y + 2 = -\frac{1}{8}x - 1\newlineSubtract 22 from both sides to get the equation in slope-intercept form:\newliney=18x12y = -\frac{1}{8}x - 1 - 2\newliney=18x3y = -\frac{1}{8}x - 3

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