Question

What's the equation in slope-intercept form for this graph?

-X values: 1, 2, 3, 4, 5
-Y values: 3, 5, 7, 9, 11

Answer 1

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

From the x and y values provided:
- X values: 1, 2, 3, 4, 5
- Y values: 3, 5, 7, 9, 11

We can calculate the slope \( m \) using the formula:

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

Let's take two points from the data: (1, 3) and (2, 5).

\[
m = \frac{5 - 3}{2 - 1} = \frac{2}{1} = 2
\]

Next, we know \( m = 2 \). Now we can use one of the points to find the y-intercept \( b \). Let's use the point (1, 3):

\[
y = mx + b
\]
\[
3 = 2(1) + b
\]
\[
3 = 2 + b
\]
\[
b = 3 - 2 = 1
\]

Now we can write the equation in slope-intercept form:

\[
y = 2x + 1
\]

Thus, the equation in slope-intercept form for the graph is:

\[
\boxed{y = 2x + 1}
\]