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.

Question

-5,6;y=1/5x-2

Write an equation for the perpendicular line in​ slope-intercept form.
​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)

Answer 1

The slope of the given line is 1/5. The slope of a line perpendicular to this line would be the negative reciprocal of 1/5, which is -5.

Using the point-slope form of a linear equation, we have:

y - y1 = m(x - x1),

where (x1, y1) is the given point and m is the slope.

Substituting (x1, y1) = (-5, 6) and m = -5, we get:

y - 6 = -5(x - (-5)).

Simplifying the equation:

y - 6 = -5(x + 5).

Expanding the bracket:

y - 6 = -5x - 25.

Rearranging the equation into slope-intercept form:

y = -5x - 19.

Therefore, the equation of the line that passes through (-5, 6) and is perpendicular to y = 1/5x - 2 is y = -5x - 19.