Write a​ slope-intercept equation for a line that passes through left parenthesis 5 comma 0 right parenthesis and left parenthesis negative 7 comma 9 right parenthesis.

To write the slope-intercept form of the equation of a line, we first need to find the slope (denoted as \( m \)) using the formula:

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

Given the points \( (5, 0) \) and \( (-7, 9) \):

\[
m = \frac{9 - 0}{-7 - 5} = \frac{9}{-12} = -\frac{3}{4}
\]

Now that we know the slope is \( -\frac{3}{4} \), we can use the point-slope form of a line equation:

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

Using the point \( (5, 0) \):

\[
y - 0 = -\frac{3}{4}(x - 5)
\]

Simplifying this:

\[
y = -\frac{3}{4}(x - 5)
\]

Distribute the \( -\frac{3}{4} \):

\[
y = -\frac{3}{4}x + \frac{15}{4}
\]

Thus, the slope-intercept form of the line equation is:

\[
y = -\frac{3}{4}x + \frac{15}{4}
\]

Would you like more details on any part of this explanation?

Here are some related questions for further exploration:
1. How do you calculate the slope if you're given two points with the same x-coordinate?
2. How does changing the slope affect the steepness of the line?
3. What is the significance of the y-intercept in a real-world context?
4. How would you graph the line \( y = -\frac{3}{4}x + \frac{15}{4} \)?
5. How can you rewrite the equation \( y = -\frac{3}{4}x + \frac{15}{4} \) in standard form?

**Tip:** To verify a line equation, substitute the given points into the equation and check if they satisfy it.

Write a slope-intercept equation for a line that passes through (5, 0) and (-7, 9).

Learn how to write the slope-intercept form equation for a line passing through points (5, 0) and (-7, 9). This detailed solution covers key algebra concepts such as calculating the slope and using the slope-intercept form, suitable for students in Grades 8-10.

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