To find the equation of a line in slope-intercept form, we need to use the formula:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Step 1: Find the slope $m$

The slope formula 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 points $(5, 5)$ and $(4, -2)$:

$m = \frac{-2 - 5}{4 - 5} = \frac{-7}{-1} = 7$

Step 2: Use the slope-intercept form

Now that we have the slope $m = 7$, substitute one of the points (we’ll use $(5, 5)$) and the slope into the equation $y = mx + b$ to find the y-intercept $b$.

$5 = 7(5) + b$

$5 = 35 + b$

$b = 5 - 35 = -30$

Step 3: Write the equation

Now that we have both the slope $m = 7$ and the y-intercept $b = -30$, the equation of the line is:

$y = 7x - 30$

This is the equation of the line in slope-intercept form.

Would you like further details or explanations?

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Here are 5 related questions:

1. What is the slope of a line that passes through the points (1, 2) and (3, 8)?
2. How do you convert the equation $2x - 3y = 6$ into slope-intercept form?
3. What is the significance of the slope in a linear equation?
4. Can a vertical line be written in slope-intercept form?
5. How do you find the y-intercept if you only know the slope and one point?

Tip: To quickly find the slope between two points, remember it’s just the "rise over run" or the change in $y$ values divided by the change in $x$ values.