Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y – 3 = (x + 2); (–2, 3)
A. Y+3= -3/8(X-2)
B.Y-3=-3/8(X+2)
C.Y-2=-3/8(X+3)
D. Y+3=3/8(X-2)
I am not sure how to do this problem...please help...
This question was supposed to have a 8/3 after the = and before the (x+2)
if it was supposed to be
y – 3 = (8/3)(x + 2)
the it has slope 8/3, so the perpendicular has slope -3/8.
just plug in the point-slope form of the line:
(y-k) = m(x-h)
y-3 = -3/8 (x+2)
B
Thank you - I understand now
To find the equation of a line that is perpendicular to the given line and passes through the given point, you need to follow a few steps:
Step 1: Determine the slope of the given line.
The given line equation is in slope-intercept form (y = mx + b), where m is the slope. Comparing the given line equation y - 3 = (x + 2) to the slope-intercept form, we can see that the slope (m) of the given line is 1.
Step 2: Find the slope of the perpendicular line.
The slope of a perpendicular line is the negative reciprocal of the slope of the given line. In this case, the negative reciprocal of 1 is -1.
Step 3: Use the point-slope form of the line to find the equation.
The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope. Plugging in the values from the given point (–2, 3) and the slope (-1) into the point-slope form, we have:
y - 3 = -1(x - (-2))
y - 3 = -1(x + 2)
y - 3 = -x - 2
Adding x and 3 to both sides of the equation, we obtain:
y + x = 1
Therefore, the equation of the line that is perpendicular to the given line y – 3 = (x + 2) and passes through the point (–2, 3) is y + x = 1.
Out of the given answer choices, none exactly match the equation we found:
A. Y+3= -3/8(X-2)
B. Y-3=-3/8(X+2)
C. Y-2=-3/8(X+3)
D. Y+3=3/8(X-2)
None of the answer choices is correct. The correct equation is y + x = 1.