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The equation for line cc can be written as y=−37x+4y = -\frac{3}{7}x + 4. Perpendicular to line cc is line dd, which passes through the point (2,4)(2,4). What is the equation of line dd?\newlineWrite 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 cc can be written as y=−37x+4y = -\frac{3}{7}x + 4. Perpendicular to line cc is line dd, which passes through the point (2,4)(2,4). What is the equation of line dd?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Perpendicular Lines Slopes: Line dd is perpendicular to line cc. Are their slopes the same or opposite reciprocals?\newlineSlopes of perpendicular lines are opposite reciprocals.
  2. Equation of Line c: Equation of line c: \newliney=−37x+4y = -\frac{3}{7}x + 4\newlineFind the slope of line c.\newlineCompare y=−37x+4y = -\frac{3}{7}x + 4 with y=mx+by = mx + b.\newlinem=−37m = -\frac{3}{7}\newlineSlope of line c: −37-\frac{3}{7}
  3. Slope of Line dd: Line dd is perpendicular to cc.\newlineSlope of line cc: −37-\frac{3}{7}\newlineFind the slope of line dd.\newlineOpposite reciprocal of −37-\frac{3}{7} is 73\frac{7}{3}.\newlineSlope of line dd: 73\frac{7}{3}
  4. Y-Intercept Calculation: For line dd: \newlineSlope (mm): 73\frac{7}{3}\newlinePoint: (2,4)(2, 4)\newlinePlug these values in y=mx+by = mx + b and find the y-intercept.\newline4=73(2)+b4 = \frac{7}{3}(2) + b\newline4=143+b4 = \frac{14}{3} + b\newline4−143=b4 - \frac{14}{3} = b\newline123−143=b\frac{12}{3} - \frac{14}{3} = b\newline−23=b-\frac{2}{3} = b
  5. Equation of Line d: For line d: \newlineSlope mm: 73\frac{7}{3}\newliney-intercept bb: −23\frac{-2}{3}\newlineWhat is the equation of the line d in slope-intercept form?\newlineSubstitute 73\frac{7}{3} for mm and −23\frac{-2}{3} for bb in y=mx+by = mx + b.\newliney=73x−23y = \frac{7}{3}x - \frac{2}{3}

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