Question

The graph shows a function of the form f(x) = ax + b. Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function. URGENT SOS

Answer 1

- When x = 0, f(x) = -5

- Each time x increases by 1, f(x) increase by 3

- f(x) = 3x - 5

Explanation:

m = slope of the graph

m =
`\frac{y_(2)-y_(1)}{x_(2)-x{1}}`

m =
`(4- (-5))/(3-0)`

m =
`(9)/(3)`

m = 3

`y - y_(1) = m ( x - x_(1))`

`y - (-5) = 3 ( x - 0 )`

`y = 3x - 5`

Answer 2

1.
`\(f(x) = -5\)`

2.
`\(f(x)\) increases by \(3\) each time \(x\) increases by \(1\).`

3.
`\(f(x) = 3x - 5\)`

1. When x = 0, the value of f(x) is:

To find the value of
`\(f(x)\)` when
`\(x = 0\)`, substitute
`\(x = 0\)` into the equation. From the point (0, -5), we get
`\(f(0) = -5\)`.

2. Each time x increases by 1, f(x) increases by:

The slope of the line
`(\(a\))` represents the rate of change of
`\(f(x)\)` concerning
`\(x\)`. From the given points (3, 4) and (0, -5), we can calculate the slope as
`\(a = \frac{\text{change in } y}{\text{change in } x} = (4 - (-5))/(3 - 0) = (9)/(3) = 3\)`. Therefore, each time
`\(x\)` increases by 1,
`\(f(x)\)` increases by 3.

3. Write an equation to model the function:

The equation for the line in slope-intercept form is
`\(f(x) = ax + b\)`. Substituting the slope
`\(a = 3\)` and using the point (0, -5) to find the y-intercept, we get
`\(f(x) = 3x - 5\)`.