We are tasked with finding the equation of a line with slope $m = 3$, passing through the point $(9, 7)$, and expressing the equation in both point-slope and slope-intercept forms.

1. Point-Slope Form:

The point-slope form of a line is given by:

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

Where:

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

Substituting the values $m = 3$, $x_1 = 9$, and $y_1 = 7$:

$y - 7 = 3(x - 9)$

Thus, the point-slope form is:

$y - 7 = 3(x - 9)$

2. Slope-Intercept Form:

The slope-intercept form is given by:

$y = mx + b$

To find $b$ (the y-intercept), we use the point $(9, 7)$ and substitute it into the equation along with $m = 3$:

$7 = 3(9) + b$

Simplifying:

$7 = 27 + b$

$b = 7 - 27 = -20$

So, the slope-intercept form is:

$y = 3x - 20$

Final Answers:

• Point-slope form: $y - 7 = 3(x - 9)$
• Slope-intercept form: $y = 3x - 20$

Would you like more details on any part of the solution?

Related Questions:

1. How can you convert from point-slope form to standard form?
2. How do you find the slope of a line if you're given two points?
3. What is the general formula for slope-intercept form?
4. How do perpendicular slopes relate to each other?
5. Can you find the equation of a line parallel to this one passing through a different point?

Tip:

Remember that in slope-intercept form, $m$ represents the slope, and $b$ represents the y-intercept (where the line crosses the y-axis).