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.
(-3,6)y=1/3x-3
To find the equation of a line that is perpendicular to the given equation, we need to find the negative reciprocal of its slope.
The given equation is in slope-intercept form y = mx + b, where m represents the slope.
The slope of the given equation is 1/3.
The negative reciprocal of 1/3 is -3.
Since the line we need to find is perpendicular to the given equation and passes through the point (-3, 6), we can use the point-slope form:
y - y1 = m(x - x1)
Using the point (-3, 6) and the slope -3:
y - 6 = -3(x - (-3))
y - 6 = -3(x + 3)
y - 6 = -3x - 9
Now, rearrange the equation in slope-intercept form y = mx + b:
y = -3x - 9 + 6
y = -3x - 3
Therefore, the equation of the line that passes through (-3, 6) and is perpendicular to y = (1/3)x - 3 is y = -3x - 3.