Question

The graph of a linear function is shown on the grid. plotted points are Y 11,12 X -4, -3

Which equation is best represented by this graph?

Answer 1

To determine the equation of the linear function represented by the given points \( Y: 11, 12 \) and \( X: -4, -3 \), we need to first find the slope of the line based on these points. The two points can be represented as the coordinates \( (-4, 11) \) and \( (-3, 12) \).

1. **Calculate the slope (m)** between the two points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 11}{-3 - (-4)} = \frac{1}{1} = 1
\]

2. **Use the point-slope form of the equation of a line**:
The point-slope form is given as:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points; let's choose \( (-4, 11) \):
\[
y - 11 = 1(x + 4)
\]

3. **Simplify the equation**:
\[
y - 11 = x + 4
\]
\[
y = x + 15
\]

Thus, the equation of the linear function best represented by the graph is:
\[
y = x + 15
\]

This is the equation of the line based on the two given points.