Question

Find the slope of the line that passes through the given points. Then determine the Vertical Intercept. Use the Slope and Vertical Intercept to write the Equation for the Line. The first one is done for you as an example.

Note: If the slope does not exist, enter DNE
ordered pairs (-9, 41) and (2, -3)
slope
vertical intercept
equation of the line

Answer 1

To find the slope of the line that passes through the points \((-9, 41)\) and \( (2, -3)\), you can use the slope formula:

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

Here, \((x_1, y_1) = (-9, 41)\) and \((x_2, y_2) = (2, -3)\).

Plugging in these values:

\[
m = \frac{-3 - 41}{2 - (-9)} = \frac{-3 - 41}{2 + 9} = \frac{-44}{11} = -4
\]

So, the slope \(m\) is \(-4\).

Next, we can find the vertical intercept (y-intercept). The vertical intercept occurs where \(x = 0\). We can use the point-slope form of a line:

\[
y - y_1 = m(x - x_1)
\]

Using one of the points, let’s use \((-9, 41)\):

\[
y - 41 = -4(x + 9)
\]

Expanding this gives:

\[
y - 41 = -4x - 36
\]

Adding 41 to both sides:

\[
y = -4x + 5
\]

Thus, the vertical intercept is \(5\).

Now we can summarize:

- **Slope:** \(-4\)
- **Vertical Intercept:** \(5\)
- **Equation of the Line:** \(y = -4x + 5\)