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.
the ordered pair (negative 2, 3) ; y equals one-half x minus 1.
(1 point)
Responses
y equals one-half x plus 1.
Image with alt text: y equals one-half x plus 1.
y equals negative two x minus 1.
Image with alt text: y equals negative two x minus 1.
y equals one-half x minus 1.
Image with alt text: y equals one-half x minus 1.
y equals negative one-half x minus 1.
To find the equation of the line that is perpendicular to the given equation, we need to find the negative reciprocal of the slope of the given equation.
The given equation is y = 1/2x - 1.
The slope of this equation is 1/2.
The negative reciprocal of 1/2 is -2.
Therefore, the equation of the line that is perpendicular to y = 1/2x - 1 and passes through the point (-2, 3) is:
y = -2x + b
To find the value of b, we can substitute the x and y values of the given point into the equation:
3 = -2(-2) + b
3 = 4 + b
b = 3 - 4
b = -1
So, the equation of the line that is perpendicular to y = 1/2x - 1 and passes through the point (-2, 3) is:
y = -2x - 1