Question㸚、] Write the linear equation that gives the rule for this table. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 5 & 9 \\ \hline 6 & 13 \\ \hline 7 & 17 \\ \hline 8 & 21 \\ \hline \end{tabular}
䯚. Write your answer as an equation with y first, followed by an equals sign. $\square$

Studdy Solution

STEP 1

1. The table represents a linear relationship between $x$ and $y$ .
2. The relationship can be expressed in the form of a linear equation $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
3. We need to determine the values of $m$ and $b$ using the given data points.

STEP 2

1. Determine the slope $m$ of the linear equation.
2. Use one of the data points to solve for the y-intercept $b$ .
3. Write the linear equation in the form $y = mx + b$ .

STEP 3

To find the slope $m$ , use the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Using the points $(5, 9)$ and $(6, 13)$ :
$m = \frac{13 - 9}{6 - 5} = \frac{4}{1} = 4$

STEP 4

Use the slope $m = 4$ and one of the points, say $(5, 9)$ , to find the y-intercept $b$ using the equation $y = mx + b$ :
Substitute $m = 4$ , $x = 5$ , and $y = 9$ :
$9 = 4(5) + b$
$9 = 20 + b$
Solve for $b$ :
$b = 9 - 20 = -11$

STEP 5

Write the linear equation using the values of $m$ and $b$ :
$y = 4x - 11$
This is the linear equation that represents the rule for the table.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms