Question

Use the graph to answer the question

The graph shows a line passing through (-2, 1) and (2, 3)

Write the equation of the line shown in the graph in slope-intercept form

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the two points given: (-2, 1) and (2, 3).

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

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

Substituting in the points (-2, 1) and (2, 3):

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

Now, we have the slope \(m = \frac{1}{2}\).

Next, we can use the point-slope form of a line equation \(y - y_1 = m(x - x_1)\) to find the equation. We can use one of the points, say (-2, 1):

\[
y - 1 = \frac{1}{2}(x - (-2))
\]
\[
y - 1 = \frac{1}{2}(x + 2)
\]

Now, simplify this equation:

\[
y - 1 = \frac{1}{2}x + 1
\]
\[
y = \frac{1}{2}x + 1 + 1
\]
\[
y = \frac{1}{2}x + 2
\]

Thus, the equation of the line in slope-intercept form is:

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