To find the rate of change, we first need to calculate the slope of the line passing through the points (0,0) and (2,3).
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0,0) for (x1, y1) and (2,3) for (x2, y2), the slope can be calculated as:
m = (3 - 0) / (2 - 0)
m = 3 / 2
m = 1.5
Therefore, the rate of change (or slope) of the line passing through the points (0,0) and (2,3) is 1.5.
To find the initial value (y-intercept) of the line, we can use the point-slope form of a linear equation:
y = mx + b
Substitute the slope (m = 1.5) and either of the points (0,0) into the equation to solve for the y-intercept (b):
0 = 1.5(0) + b
0 = 0 + b
b = 0
Therefore, the initial value (y-intercept) of the line passing through the points (0,0) and (2,3) is 0.
In conclusion, the rate of change of the line is 1.5 and the initial value is 0.
(0,0) (2,3)
What is the rate of change and initial value?
1 answer