Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(- 5, 7); y = 1/5 * x - 4
Write an equation for the perpendicular line in slope-intercept form.
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(Simplify your answer. Use integers or fractions for any numbers in the equation.)
To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The slope of the given line is 1/5, so the negative reciprocal is -5/1 or -5.
We also know that the line passes through the point (-5, 7).
Using the point-slope form of a line, we can substitute the values into the equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
y - 7 = -5(x - (-5))
y - 7 = -5(x + 5)
y - 7 = -5x - 25
To write the equation in slope-intercept form (y = mx + b), we need to isolate y:
y = -5x - 25 + 7
y = -5x - 18
Therefore, the equation of the perpendicular line in slope-intercept form is y = -5x - 18.