Questions: A linear function is shown in the table below. Find its slope, (y)-intercept, and formula in slope-intercept form. Note this is sample data. (x) -15 -10 -5 0 5 10 15 (mathbfy) -29 -19 -9 1 11 21 31 Slope (=) y -intercept: (Remember that the (y)-intercept is a point.) [ hatmathrmy= ]

Solution Steps

To find the slope of the linear function, we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), which is \((y_2 - y_1) / (x_2 - x_1)\). We can choose any two points from the table to calculate this. The y-intercept is the value of \(y\) when \(x = 0\), which can be directly read from the table. Finally, the formula in slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

To find the slope \( m \) of the linear function, we can use the formula:

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

Using the points \((-15, -29)\) and \((-10, -19)\):

\[ m = \frac{-19 - (-29)}{-10 - (-15)} = \frac{10}{5} = 2.0 \]

The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, we see that:

\[ b = 1 \]

The slope-intercept form of a linear equation is given by:

\[ \hat{y} = mx + b \]

Substituting the values of \( m \) and \( b \):

\[ \hat{y} = 2.0x + 1 \]

Final Answer