Question

The graph of a linear function is shown on the grid. plotted points are Y 12,11 X -3, -4
Which equation is best represented by this graph?.

USE THE NUMBER PLOTTED

Answer 1

To find the equation of the linear function based on the points provided, we first need to identify the coordinates of the two points you've given:

1. Point 1: \(Y (12, 11)\) → This appears to be written incorrectly as this should be two separate points. Assuming you meant:
- Point A: (12, Y)
- Point B: (11, Y)

But we will interpret "Y 12, 11" as points in the graph which should be
- Point A: \((-3, 11)\)
- Point B: \((-4, 12)\)

2. Point 2: \(X (-3, -4)\) → Let's assume this also represents the x-coordinates for the points we are considering.

Given the assumed points (-3, 11) and (-4, 12), we can find the slope (m) of the linear function using the formula:

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

Substituting the points in, we have:
\[
m = \frac{12 - 11}{-4 - (-3)} = \frac{1}{-1} = -1
\]

Next, we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using Point A \((-3, 11)\):
\[
y - 11 = -1(x + 3)
\]

Expanding this gives:
\[
y - 11 = -x - 3
\]
\[
y = -x + 8
\]

Thus, the equation of the line represented by the points (-3, 11) and (-4, 12) is:

\[
y = -x + 8
\]

If the points given were interpreted differently, please clarify the points, and I can help you find the correct linear equation.