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.
(-2, 3); y = 1/2x - 1
The given equation is in the form y = mx + b, where m is the slope of the line. In this case, the given equation has a slope of 1/2.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the line perpendicular to y = 1/2x - 1 would be -2 (negative reciprocal of 1/2).
We can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
Using the given point (-2, 3) and the slope -2, the equation becomes:
y - 3 = -2(x - (-2))
Simplifying:
y - 3 = -2(x + 2)
y - 3 = -2x - 4
y = -2x - 4 + 3
y = -2x - 1
Therefore, the equation in slope-intercept form of the line that passes through (-2, 3) and is perpendicular to y = 1/2x - 1 is y = -2x - 1.