The problem states:

"It passes through (7, 3) and has a slope of 5."

We are asked to find the equation of the line that passes through the point $(7, 3)$ and has a slope $m = 5$.

Solution:

We can use the point-slope form of a line, which is given by:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope
• $(x_1, y_1)$ is the point the line passes through

Substituting the given point $(7, 3)$ and the slope $m = 5$ into the equation:

$y - 3 = 5(x - 7)$

Now, simplify this equation:

$y - 3 = 5x - 35$

Add 3 to both sides:

$y = 5x - 32$

Final Equation:

The equation of the line is:

$y = 5x - 32$

Would you like more details on any step or have further questions?

Here are 5 related questions to explore:

1. How do you convert the point-slope form to slope-intercept form?
2. What is the general form of a linear equation, and how would this equation be written in that form?
3. How would you find the y-intercept if it wasn't already apparent in the slope-intercept form?
4. What would the graph of this line look like, and how would the point (7, 3) appear on it?
5. Can we use other methods, like the two-point form, to verify the equation of the line?

Tip: When dealing with lines, remembering the point-slope form is a quick way to get the equation when you're given a point and slope!