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 points \( (X, Y) = (-4, 11) \) and \( (-3, 12) \), we can first find the slope of the line. The slope \( m \) is calculated using the formula:

\[
m = \frac{Y_2 - Y_1}{X_2 - X_1}
\]

Using the points \( (-4, 11) \) as \( (X_1, Y_1) \) and \( (-3, 12) \) as \( (X_2, Y_2) \):

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

The slope \( m \) is \( 1 \).

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

\[
Y - Y_1 = m(X - X_1)
\]

Using the point \( (-4, 11) \):

\[
Y - 11 = 1(X - (-4))
\]

This simplifies to:

\[
Y - 11 = X + 4
\]

Adding 11 to both sides:

\[
Y = X + 15
\]

Thus, the equation of the line is:

\[
Y = X + 15
\]

This is the best representation of the linear function based on the plotted points.