Question

Write an equation from slope-intercept form( y=mx+b ) from the table below.
x-y
2-11
4-19
6-27

Answer 1

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

1. **Calculate the slope \( m \)**:
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We can use any two points from the table. Let's use the points (2, 11) and (4, 19).

- \( (x_1, y_1) = (2, 11) \)
- \( (x_2, y_2) = (4, 19) \)

Substitute into the slope formula:
\[
m = \frac{19 - 11}{4 - 2} = \frac{8}{2} = 4
\]

2. **Find the y-intercept \( b \)**:
We can use one of the points to find \( b \). Using the point (2, 11) and knowing \( m = 4 \):
\[
y = mx + b
\]
Substitute the known values:
\[
11 = 4(2) + b
\]
Simplify:
\[
11 = 8 + b
\]
Solving for \( b \):
\[
b = 11 - 8 = 3
\]

3. **Write the equation in slope-intercept form**:
Now that we have \( m = 4 \) and \( b = 3 \), the equation is:
\[
y = 4x + 3
\]

So, the equation from the given table is:
\[
y = 4x + 3
\]