Write the equation of the line containing (-3,4) and perpendicular to y = 2/3x + 2.
Write your answer in slope-intercept form.
Not sure how to do this one.
please help.
To find the equation of a line perpendicular to another line, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
First, let's find the slope of the given line y = (2/3)x + 2. The slope-intercept form of a line is y = mx + b, where m is the slope. Comparing this equation with the given equation, we see that the slope of the given line is 2/3.
The negative reciprocal of 2/3 is -3/2. So, the slope of the line perpendicular to y = (2/3)x + 2 will be -3/2.
Now, we have the slope of the line perpendicular to the given line. We also know that this line passes through the point (-3,4).
To find the equation of the line, we can use the point-slope form of a line, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the values, we have:
y - 4 = (-3/2)(x - (-3))
Simplifying:
y - 4 = (-3/2)(x + 3)
y - 4 = (-3/2)x - (9/2)
y = (-3/2)x - (9/2) + 4
y = (-3/2)x - (9/2) + 8/2
y = (-3/2)x - 1/2
So, the equation of the line containing (-3,4) and perpendicular to y = (2/3)x + 2 is y = (-3/2)x - 1/2 in slope-intercept form.