(Graphing Linear Equations LC)
Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
To determine which graph has a slope of -3/2 and a y-intercept of 2, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
The equation of the line with a slope of -3/2 and a y-intercept of 2 is: y = (-3/2)x + 2
Let's check each graph to see which one best represents this equation:
1. graph of a line passing through the points 0,2 and 3,0:
The slope of this line is (0-2)/(3-0) = -2/3, which is not equal to -3/2. Therefore, this graph does not represent the given equation.
2. graph of a line passing through the points 0,2 and 2,-1:
The slope of this line is (2-(-1))/(0-2) = 3/2, which is not equal to -3/2. Therefore, this graph does not represent the given equation.
3. graph of a line passing through the points 0,3 and 2,0:
The slope of this line is (3-0)/(0-2) = 3/(-2) = -3/2. The y-intercept is 3.
This graph represents the given equation: y = (-3/2)x + 3.
However, the y-intercept is 3, not 2, so this graph does not have a y-intercept of 2.
4. graph of a line passing through the points 0,3 and 3,1:
The slope of this line is (3-1)/(0-3) = 2/(-3) = -2/3, which is not equal to -3/2. Therefore, this graph does not represent the given equation.
None of the given graphs represent a line with a slope of -3/2 and a y-intercept of 2.