Question

Write the equation of the linear function shown on the graph. (2,4) ,(-3,-1) enter your answer in y=mx+b

Answer 1

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

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

Let's assign the points:
- Point 1 (x₁, y₁) = (2, 4)
- Point 2 (x₂, y₂) = (-3, -1)

Now substituting the coordinates into the slope formula:

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

The slope (m) is 1.

Next, we will use the point-slope form of the equation of a line, \(y - y_1 = m(x - x_1)\), to find the equation. We can use either of the two points; we'll use (2, 4):

\[
y - 4 = 1(x - 2)
\]

Expanding this gives:

\[
y - 4 = x - 2
\]

Now, add 4 to both sides:

\[
y = x + 2
\]

Thus, the equation of the linear function is:

\[
y = 1x + 2 \quad \text{or simply} \quad y = x + 2
\]

This is the final equation in the form \(y = mx + b\).