Question

The graph of a linear function is shown on the grid. Which equation is best represented by this graph? the graph has a point at (-6, 3) and (3, -3)

Answer 1

To determine the equation of the linear function represented by the points (-6, 3) and (3, -3), we can follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can take the two points as \((x_1, y_1) = (-6, 3)\) and \((x_2, y_2) = (3, -3)\).

\[
m = \frac{-3 - 3}{3 - (-6)} = \frac{-6}{3 + 6} = \frac{-6}{9} = -\frac{2}{3}
\]

2. **Find the y-intercept (b)** using the slope-intercept form of the line equation \(y = mx + b\). We can use one of the points to solve for \(b\). Let's use the point (3, -3):
\[
-3 = -\frac{2}{3}(3) + b
\]
\[
-3 = -2 + b
\]
\[
b = -3 + 2 = -1
\]

3. **Write the equation** of the line in slope-intercept form:
\[
y = -\frac{2}{3}x - 1
\]

Thus, the equation that best represents the graph is:

\[
y = -\frac{2}{3}x - 1
\]