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

1 answer

It seems you're trying to describe a linear function based on some plotted points. However, the coordinates you've provided are a bit unclear, especially the way you've formatted them. I’ll interpret your description as two points on the Cartesian plane:

  1. Point \( Y \) (which I assume means a point on the graph) is at \( (12, 11) \).
  2. Point \( X \) is at \( (-3, -4) \).

If these are indeed the two points on the graph, we can find the equation of the linear function that passes through these two points.

The general form of a line is:

\[ y = mx + b \]

Where \( m \) is the slope. To find the slope \( m \), we can use the formula:

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

Substituting the values:

  • \( (x_1, y_1) = (-3, -4) \)
  • \( (x_2, y_2) = (12, 11) \)

Calculating the slope:

\[ m = \frac{11 - (-4)}{12 - (-3)} = \frac{11 + 4}{12 + 3} = \frac{15}{15} = 1 \]

Now, we know the slope \( m = 1 \).

Next, we can use one of the points to solve for \( b \). We'll use point \( (12, 11) \):

\[ y = mx + b \ 11 = 1 \cdot 12 + b \ 11 = 12 + b \ b = 11 - 12 = -1 \]

So, the equation of the linear function is:

\[ y = 1x - 1 \quad \text{or simply} \quad y = x - 1 \]

If this interpretation isn't what you were looking for, please clarify the points and their coordinates, and I'll be happy to assist further!