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rusak2 [61]
3 years ago
6

Write an equation for a line perpendicular to y = -5x – 4 and passing through the point (15,5)

Mathematics
1 answer:
3241004551 [841]3 years ago
7 0

The equation for the line in point-slope form that passes through (15, 5) and is perpendicular to y = -5x - 4 is \mathbf{y -5 = \frac{1}{5} (x - 15)}

<em><u>Recall:</u></em>

The equation of the line can be written in point-slope form (y - b = m(x - a)) and also in slope-intercept form (y = mx + b).

<em><u>Given</u></em>:

  • the point the line passes through: (15, 5)
  • the line it is perpendicular to: y = -5x - 4

<u><em>Find the </em></u><u><em>slope (m):</em></u>

The slope value will be the negative reciprocal of the slope value of y = -5x - 4.

  • The slope of y = -5x - 4 is -5.

  • Therefore, the slope of the line perpendicular to y = -5x - 4 will be the negative reciprocal of -5 which is: 1/2.

<em>Write the </em><em>equation </em><em>in </em><em>point-slope</em><em> form by substituting m = 1/2 and (a, b) = (15, 5) into </em><em>y - b = m(x - a)</em>

<em />

  • Thus:

y -5 = \frac{1}{5} (x - 15)

Therefore, the equation for the line that passes through (15, 5) and is perpendicular to y = -5x - 4 is \mathbf{y -5 = \frac{1}{5} (x - 15)}

Learn more here:

brainly.com/question/11624671

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