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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?.

3 answers

To determine the equation of the linear function represented by the points Y(12, 11) and X(-3, -4), we first need to find the slope (m) of the line that passes through these two points.

  1. Finding the slope (m): The slope is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (x1, y1) = (-3, 12) and (x2, y2) = (-4, 11): \[ m = \frac{11 - 12}{-4 - (-3)} = \frac{-1}{-1} = 1 \]

  2. Finding the y-intercept (b): We can use the slope-intercept form of the line: \[ y = mx + b \] Now we can plug in one of the points to find b. Let's use the point (-3, 12): \[ 12 = 1(-3) + b \] \[ 12 = -3 + b \] \[ b = 12 + 3 = 15 \]

  3. Writing the equation: Now that we have the slope (m = 1) and the y-intercept (b = 15), we can write the equation of the line: \[ y = 1x + 15 \] or simply \[ y = x + 15 \]

Thus, the equation best represented by the graph is:

\[ y = x + 15 \]

wrong

I apologize for the oversight. Let’s correctly find the equation of the linear function using the provided points more carefully.

You mentioned the points \( (Y, 12, 11) \) and \( (X, -3, -4) \), which seem to indicate two separate points on the graph. Let's clarify the points as follows:

  1. Identify the Points:

    • Let’s assume the points are \((-3, 12)\) and \((-4, 11)\).

  2. Calculate the Slope (m): The slope \(m\) is calculated with the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For points \( (-3, 12) \) and \( (-4, 11) \): \[ (x_1, y_1) = (-3, 12) \quad \text{and} \quad (x_2, y_2) = (-4, 11) \] \[ m = \frac{11 - 12}{-4 - (-3)} = \frac{-1}{-4 + 3} = \frac{-1}{-1} = 1 \]

  3. Finding the y-intercept (b): Now we use the slope-intercept form of the line \( y = mx + b \). Plug in the slope and one of the points to solve for \(b\). Let’s use the point \( (-3, 12) \): \[ 12 = 1(-3) + b \] \[ 12 = -3 + b \] \[ b = 12 + 3 = 15 \]

  4. Equation of the Line: Thus, the equation based on the points should be: \[ y = 1x + 15 \quad \text{or} \quad y = x + 15 \] However, since you're indicating that the initial calculation is wrong, let’s carefully verify if I misunderstood the points.

Let's Re-evaluate the Points:

If the points were \( (x_1, y_1) = (-3, 12) \) and \( (x_2, y_2) = (-4, 11) \):

  • The y-coordinates reflect vertical points.
  • The slope is calculated based on the definition: \( \text{slope} = \frac{\Delta y}{\Delta x} \)
  • Ensure that they are consistent in the explanation of points.

If you have specific corrections on how I interpreted those points or need new points to clarify, please provide them so I can assist you correctly. Thank you!