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 5, 0) ; y plus 1 equals two times left parenthesis x minus 3 right parenthesis
(1 point)
Responses
y equals negative one-half x plus 5.
Image with alt text: y equals negative one-half x plus 5.
y equals two x minus 5.
Image with alt text: y equals two x minus 5.
y equals one-half x minus 2.
Image with alt text: y equals one-half x minus 2.
y equals negative one-half x plus five-halves.
To find the equation of a line that is perpendicular to the given equation, we need to determine the slope of the given equation and then find the negative reciprocal of that slope.
The given equation is y + 1 = 2(x - 3).
To write it in slope-intercept form (y = mx + b), we need to isolate y:
y + 1 = 2x - 6
y = 2x - 6 - 1
y = 2x - 7
The slope of this equation is 2. The negative reciprocal of 2 is -1/2.
Now we can use the point(-5, 0) and the slope -1/2 to find the equation of the line using the point-slope formula:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 0 = -1/2(x - (-5))
y = -1/2(x + 5)
y = -1/2x - 5/2
Therefore, the equation of the line that passes through the point (-5, 0) and is perpendicular to the given equation is y = -1/2x - 5/2.