To solve this problem, we are asked to write the equation of a line in slope-intercept form, which is typically given as:

$y = mx + b$

Where:

• $m$ is the slope of the line, and
• $b$ is the y-intercept.

Given information:

• x-intercept = $(-6, 0)$
• y-intercept = $(0, 5)$

Step 1: Find the slope ($m$)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given intercept points:

• $(x_1, y_1) = (-6, 0)$
• $(x_2, y_2) = (0, 5)$

$m = \frac{5 - 0}{0 - (-6)} = \frac{5}{6}$

Step 2: Write the equation

Now that we have the slope $m = \frac{5}{6}$ and the y-intercept $b = 5$, we can write the equation of the line in slope-intercept form:

$y = \frac{5}{6}x + 5$

This is the equation of the line. Would you like a more detailed breakdown, or do you have any questions?

Related Questions:

1. What is the equation of a line if the x-intercept is $(4, 0)$ and the y-intercept is $(0, 7)$?
2. How does the slope affect the angle of a line with respect to the x-axis?
3. Can you find the equation of a line passing through points $(1, 2)$ and $(4, 6)$?
4. What is the equation of a vertical line that passes through the point $(-6, 5)$?
5. How would you write the equation if the slope is negative and the intercept is $(0, -3)$?

Tip:

Remember, the slope $m$ tells you how much the line rises or falls for each unit increase in $x$. The y-intercept $b$ is where the line crosses the y-axis.