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

1 answer

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.