Question

Write a linear equation in the form of y = mx + b for the following table.
x. y.
-5. 2.
-10. 16.
-15. 30.



y=___x+_____

Answer 1

To find the linear equation in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

Given the points from the table:

1. \( (-5, 2) \)
2. \( (-10, 16) \)
3. \( (-15, 30) \)

We can use two points to calculate the slope \( m \). The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the points \( (-5, 2) \) and \( (-10, 16) \):

\[
m = \frac{16 - 2}{-10 - (-5)} = \frac{14}{-5} = -\frac{14}{5}
\]

Now that we have the slope \( m = -\frac{14}{5} \), we can use one of the points to find the y-intercept \( b \). Let's use the point \( (-5, 2) \):

We can plug in the values into the equation \( y = mx + b \):

\[
2 = -\frac{14}{5}(-5) + b
\]

Calculating this, we have:

\[
2 = 14 + b
\]

Now, solving for \( b \):

\[
b = 2 - 14
\]
\[
b = -12
\]

So, the linear equation in the form \( y = mx + b \) is:

\[
y = -\frac{14}{5}x - 12
\]

Thus, the final equation is:

\[
\boxed{y = -\frac{14}{5}x - 12}
\]