Question

Write the equation of the linear function shown on the graph. use -3,-1 and 2,4 Enter your answer in y=mx+b
form.

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Answer 1

To find the equation of the linear function, we first need to calculate the slope (m) using the two points given: (-3, -1) and (2, 4).

The formula for the slope \( m \) is given by:

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

Using the points (-3, -1) (which we'll call \( (x_1, y_1) \)) and (2, 4) (which we'll call \( (x_2, y_2) \)), we can substitute:

\[
m = \frac{4 - (-1)}{2 - (-3)} = \frac{4 + 1}{2 + 3} = \frac{5}{5} = 1
\]

Now that we have the slope \( m = 1 \), we can use the slope-intercept form of the equation, \( y = mx + b \). We can substitute one of the points to find \( b \). We'll use the point (2, 4):

\[
4 = 1(2) + b
\]
\[
4 = 2 + b
\]
\[
b = 4 - 2 = 2
\]

Now we can write the equation of the line as:

\[
y = 1x + 2
\]

This simplifies to:

\[
y = x + 2
\]

So, the equation of the linear function is:

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