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The equation for line kk can be written as y=−15x−3y = -\frac{1}{5}x - 3. Perpendicular to line kk is line , which passes through the point (1,−5)(1,-5). What is the equation of line ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Q. The equation for line kk can be written as y=−15x−3y = -\frac{1}{5}x - 3. Perpendicular to line kk is line , which passes through the point (1,−5)(1,-5). What is the equation of line ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Determine Slope of Line: Determine the slope of line kk. The equation of line kk is given as y=−15x−3y = -\frac{1}{5}x - 3. The slope (mm) of a line in the slope-intercept form y=mx+by = mx + b is the coefficient of xx. Therefore, the slope of line kk is −15-\frac{1}{5}.
  2. Find Perpendicular Slope: Find the slope of the line perpendicular to line kk. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. The negative reciprocal of −15-\frac{1}{5} is 51\frac{5}{1}, or simply 55.
  3. Use Point-Slope Form: Use the point-slope form to find the equation of the perpendicular line.\newlineThe point-slope form of a line is y−y1=m(x−x1)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 have the slope of the perpendicular line as 55 and the point (1,−5)(1, -5). Plugging these into the point-slope form gives us y−(−5)=5(x−1)y - (-5) = 5(x - 1).
  4. Simplify to Intercept Form: Simplify the equation to slope-intercept form.\newlineStarting with y+5=5(x−1)y + 5 = 5(x - 1), we distribute the 55 on the right side to get y+5=5x−5y + 5 = 5x - 5. Then, we subtract 55 from both sides to isolate yy, resulting in y=5x−10y = 5x - 10.

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