Question

(0,0) (2,3)

What is the rate of change and initial value?

Answer 1

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.