two lines past through point (2,4) Line 1 passes through (-2,1) while line 2 passes through (4,0). What is the slope of one of these lines?
The line through (2,4) and (-2,1) has slope 3/4
The line through (2,4) and (4,0) has slope -2
Remember that the slope is
y2-y1
------
x2-x1
So you can use the slope formula even when you aren't given exact points?
of course not. You have to have two points.
To find the slope of a line, we can use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Let's find the slope of Line 1:
Coordinates of Point A on Line 1: (-2, 1)
Coordinates of Point B on Line 1: (2, 4)
Change in x-coordinates: 2 - (-2) = 4
Change in y-coordinates: 4 - 1 = 3
Slope of Line 1 = (change in y-coordinates) / (change in x-coordinates) = 3 / 4 = 0.75.
Therefore, the slope of Line 1 is 0.75.
Similarly, to find the slope of Line 2:
Coordinates of Point C on Line 2: (4, 0)
Coordinates of Point D on Line 2: (2, 4)
Change in x-coordinates: 2 - 4 = -2
Change in y-coordinates: 4 - 0 = 4
Slope of Line 2 = (change in y-coordinates) / (change in x-coordinates) = 4 / -2 = -2.
Therefore, the slope of Line 2 is -2.