The equation for the line in point-slope form that passes through (15, 5) and is perpendicular to [tex]y = -5x - 4[/tex] is [tex]\mathbf{y -5 = \frac{1}{5} (x - 15)}[/tex]
Recall:
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).
Given:
- the point the line passes through: (15, 5)
- the line it is perpendicular to: y = -5x - 4
Find the slope (m):
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.
Write the equation in point-slope form by substituting m = 1/2 and (a, b) = (15, 5) into y - b = m(x - a)
[tex]y -5 = \frac{1}{5} (x - 15)[/tex]
Therefore, the equation for the line that passes through (15, 5) and is perpendicular to [tex]y = -5x - 4[/tex] is [tex]\mathbf{y -5 = \frac{1}{5} (x - 15)}[/tex]
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