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.
(-4,8);y=1/4x-1
Write an equation for the perpendicular line in slope-intercept form.
To find the slope of the given equation, we can observe that the given equation is already in slope-intercept form, y = mx + b, where m is the slope. Therefore, the slope of the given equation is 1/4.
To find the slope of the perpendicular line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 1/4 is -4/1, or simply -4.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line, y - y₁ = m(x - x₁), to find the equation of the perpendicular line. Plugging in the given point (-4, 8), we have:
y - 8 = -4(x - (-4))
y - 8 = -4(x + 4)
y - 8 = -4x - 16
y = -4x - 16 + 8
y = -4x - 8
Therefore, the equation in slope-intercept form of the line that passes through the point (-4, 8) and is perpendicular to the graph of y = 1/4x - 1 is y = -4x - 8.