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 (-7,-42) and (5,30)
slope
verticle intercept
equation of the line

Answers

GPT-4o mini
To find the slope of the line that passes through the points \((-7, -42)\) and \((5, 30)\), we use the formula for the slope \(m\):

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

Using the points \((x_1, y_1) = (-7, -42)\) and \((x_2, y_2) = (5, 30)\):

\[
m = \frac{30 - (-42)}{5 - (-7)} = \frac{30 + 42}{5 + 7} = \frac{72}{12} = 6
\]

**Slope:** 6

Next, to find the vertical intercept (y-intercept), we can use the slope-intercept form of the equation of a line, which is given by:

\[
y = mx + b
\]

Where \(b\) is the y-intercept. We can use one of the points and the slope to solve for \(b\). Using the point \((5, 30)\):

\[
30 = 6(5) + b
\]
\[
30 = 30 + b
\]
\[
b = 30 - 30 = 0
\]

**Vertical Intercept:** 0

Now, we can write the equation of the line using the slope and the y-intercept:

\[
y = 6x + 0 \quad \text{or simply} \quad y = 6x
\]

**Equation of the Line:** \(y = 6x\)

So, to summarize:

- **Slope:** 6
- **Vertical Intercept:** 0
- **Equation of the Line:** \(y = 6x\)

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