Which of the following lines is perpendicular to the line x + y = 3?
a.)3y + 3x = 1
b.)y = x + 1/2
c.)y = -x + 3
y = -x + 3 so m = -1
so c
Thanks:)
To find a line that is perpendicular to the line x + y = 3, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope.
First, let's rearrange the given line in the slope-intercept form:
x + y = 3
y = -x + 3
The slope of this line is -1.
Recall that two lines are perpendicular if and only if the product of their slopes is -1.
Now, let's evaluate the slopes of the given options:
a.) 3y + 3x = 1
Rearranging, we get: y = -x + 1/3
The slope of this line is -1, so it is perpendicular to the given line.
b.) y = x + 1/2
The slope of this line is 1, which is not perpendicular to the given line.
c.) y = -x + 3
The slope of this line is -1, so it is perpendicular to the given line.
Therefore, the lines a.) and c.) are both perpendicular to the line x + y = 3.