Question

Use the graph to answer the question

The graph shows a line passing through (-6, -6) and (2, 5)

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

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) using the two points provided: (-6, -6) and (2, 5).

The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let:
- \( (x_1, y_1) = (-6, -6) \)
- \( (x_2, y_2) = (2, 5) \)

Substituting the points into the slope formula gives:
\[
m = \frac{5 - (-6)}{2 - (-6)} = \frac{5 + 6}{2 + 6} = \frac{11}{8}
\]

Now that we have the slope \( m = \frac{11}{8} \), we can use one of the points to find the y-intercept (b). We'll use the point (2, 5).

The slope-intercept form is:
\[
y = mx + b
\]

Substituting the known values:
\[
5 = \frac{11}{8}(2) + b
\]
\[
5 = \frac{22}{8} + b
\]
\[
5 = \frac{11}{4} + b
\]

To isolate \( b \), we can subtract \( \frac{11}{4} \) from both sides. First, convert 5 to a fraction with a denominator of 4:
\[
5 = \frac{20}{4}
\]
Now rearranging gives:
\[
\frac{20}{4} - \frac{11}{4} = b
\]
\[
b = \frac{9}{4}
\]

Now we have the slope and the y-intercept. The equation of the line in slope-intercept form is:
\[
y = \frac{11}{8}x + \frac{9}{4}
\]