Write a slope-intercept equation of the line whose graph is described. Perpendicular to the graph of y = x; y-intercept (0,0).
Any line perpendicular to y=x is
y=-x+k where k is a constant to be determined.
Since it passes through (0,0), we have
0=-0+k so k=0.
The line is therefore
y=-x
To find the slope-intercept equation of a line perpendicular to the graph of y = x, you need to determine the slope of the original line and then use its negative reciprocal as the slope of the perpendicular line.
For the original line y = x, the slope is 1. The negative reciprocal of 1 is -1. Therefore, the slope of the perpendicular line is -1.
Now, we have the slope of the perpendicular line (-1) and the y-intercept (0,0).
Using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept, we can substitute the given values to get the equation of the perpendicular line:
y = (-1)x + 0
Simplifying the equation, we have:
y = -x
So, the slope-intercept equation of the line that is perpendicular to the graph of y = x and passes through the y-intercept (0,0) is y = -x.