Question

Help me determine the slope (rate of change) and the y intercept (initial value) for this one! You can use the formula y = mx + b or m = y2-y1/x2-x1

Answer 1

Therefore, the equation of the line is y = 1/4x + 10, where the slope is 1/4 and the y-intercept is 10.

How to find the slope and y-intercept of a line?

To determine the slope (m) and the y-intercept (b), you can use the formula
`m = (y_2 - y_1)/(x_2 - x_1)`.

Given two points on the line:
`P_1(20, 15)\) and \(P_2(40, 20)`.

`m = (20 - 15)/(40 - 20)`

m = 5/20

Simplify the fraction:

m = 1/4

So, the slope (m) is 1/4.

Now that you have the slope, you can use one of the points and the slope in the equation y = mx + b to find the y-intercept (b). Let's use point
`P_1(20, 15)`:

`15 = (1)/(4) \cdot 20 + b`

15 = 5 + b

Subtract 5 from both sides:

b = 10

So, the y-intercept (b) is 10.