Question

The table shows values for a linear function, . What is an equation for ? Complete the equation below with the correct values. Not all numbers listed will be used.

Answer 1

`\sf f(x) = (3)/(4)x - (29)/(4)`

Explanation:

The table which shows values for a linear function is:

x: -1, 3, 7, 11

f(x): -8, -5, -2, 1

To find the equation of a linear function, we can use the point-slope form of a linear equation, which is:

`\sf f(x) = mx + b`

Where:

• f(x) is the dependent variable
• x is the independent variable
• m is the slope of the line
• b is the y-intercept

To find the values of m and b using the given data, we can choose any two points from the table.

Let's use the points (-1, -8) and (3, -5):

First, calculate the slope(m) using the formula:

`\sf Slope(m) = \frac{\text{change in } f(x)}{\text{change in } x}\\\\ = (-5 - (-8))/(3 - (-1)) \\\\\ =(3)/(4)`

Now that you have the slope (m) , we can use one of the points (let's use (-1, -8) to find the y-intercept (b).

Substitute the values into the equation:

`\sf -8 = (3)/(4)(-1) + b`

Solve for b:

`\sf -8 = -(3)/(4) + b`

Add
`\sf frac{3}{4}` to both sides:

`\sf b = -(8)/(1) + (3)/(4) \\\\ b = -(32)/(4) + (3)/(4) \\\\ b = -(29)/(4)`

So,

`\sf b = -(29)/(4)`

Now that we have the values of m and b, we can write the equation for the linear function:

`\sf f(x) = (3)/(4)x - (29)/(4)`

This is the equation for the linear function that represents the given data.