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.
(-4,3);y=1/4x-3
To find the equation of a line perpendicular to the given equation, we need to find its slope.
The given equation is y = 1/4x - 3.
The slope of this line is 1/4.
Since the line we want is perpendicular, the slope of our line will be the negative reciprocal of 1/4.
The negative reciprocal of 1/4 is -4/1 or -4.
Now we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point.
Substituting the given point (-4, 3) and the slope -4 into the equation, we get:
y - 3 = -4(x - (-4))
Simplifying:
y - 3 = -4(x + 4)
Expanding the brackets:
y - 3 = -4x - 16
Bringing the -4x to the left side:
y + 4x = -13
Finally, rearranging the equation to slope-intercept form (y = mx + b):
4x + y = -13
So the equation of the line passing through the point (-4, 3) and perpendicular to y = 1/4x - 3 is 4x + y = -13.