Which graph has a slope of Two-thirds?
On a coordinate plane, a line goes through points (0, negative 1) and (2, 2).
On a coordinate plane, a line goes through points (negative 3, 1) and (0, negative 1).
On a coordinate plane, a line goes through points (0, negative 1) and (3, 1).
On a coordinate plane, a line goes through points (negative 2, 2) and (0, negative 1).
The graph that has a slope of two-thirds is the one that goes through points (0, -1) and (3, 1).
To determine which graph has a slope of two-thirds, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slopes for each set of points:
For the line going through points (0, -1) and (2, 2):
m = (2 - (-1)) / (2 - 0) = 3 / 2 = 1.5
For the line going through points (-3, 1) and (0, -1):
m = (-1 - 1) / (0 - (-3)) = -2 / 3 = -0.6667
For the line going through points (0, -1) and (3, 1):
m = (1 - (-1)) / (3 - 0) = 2 / 3 = 0.6667
For the line going through points (-2, 2) and (0, -1):
m = (-1 - 2) / (0 - (-2)) = -3 / 2 = -1.5
Based on these calculations, the line that has a slope of two-thirds is the line going through points (0, -1) and (3, 1). Therefore, the correct graph is the option: "On a coordinate plane, a line goes through points (0, -1) and (3, 1)."