Question

Write a linear equation in the form of y = mx + b for the following table. Click Here for Help Video




x

y
0
8
5
-

−10
10

−
-28




𝑦
=
y=

𝑥
x
+
+

Answer 1

To write a linear equation in the form \( y = mx + b \), we first need to identify the values given in the table. The table has the points:

- When \( x = 0 \), \( y = 8 \)
- When \( x = 5 \), \( y = -10 \)
- When \( x = 10 \), \( y = -28 \)

We can use any two points to calculate the slope \( m \) and then use one of the points to solve for \( b \) (the y-intercept).

Let's use the points \( (0, 8) \) and \( (5, -10) \).

### Step 1: Calculate the Slope (m)

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

Using the points \( (0, 8) \) and \( (5, -10) \):

- \( x_1 = 0, y_1 = 8 \)
- \( x_2 = 5, y_2 = -10 \)

\[
m = \frac{-10 - 8}{5 - 0} = \frac{-18}{5} = -\frac{18}{5}
\]

### Step 2: Solve for the y-intercept (b)

Using the slope-intercept form \( y = mx + b \) and the point \( (0, 8) \):

\[
8 = -\frac{18}{5}(0) + b
\]
\[
b = 8
\]

### Step 3: Write the Linear Equation

Now, we can write the equation of the line:

\[
y = -\frac{18}{5}x + 8
\]

This is your linear equation in the form of \( y = mx + b \).

Therefore, the final answer is:

\[
y = -\frac{18}{5}x + 8
\]