We want to find the initial value and rate of change of the given line. We will see that the initial value is 1 and the rate of change is 3/5.
General line equation.
A general line equation is given by:
y = a*x + b
Where we can define a as the rate of change (also called the slope) and b as the initial value (also called the y-intercept).
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Here we know that:
- The line passes through the y-intercept at 1
- The line passes through the point (5, 4).
So we know that the y-intercept is y = 1, so the line passes through the point (0, 1). Then we already know the initial value.
And with these two points we can find the rate of change or slope:
[tex]a = \frac{4 - 1}{5} = \frac{3}{5} [/tex]
So the initial value is 1 and the rate of change is 3/5.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4074386
