To find the equation of the line in slope-intercept form ($y = mx + b$), we are given:

• Slope ($m$): $-3$
• Point ($x_1, y_1$): $(-7, 1)$

Step 1: Use the Point-Slope Formula

The point-slope formula is: $y - y_1 = m(x - x_1)$

Step 2: Plug in the Given Values

$y - 1 = -3(x + 7)$

Step 3: Expand the Equation

Distribute the $-3$: $y - 1 = -3x - 21$

Step 4: Isolate $y$

$y = -3x - 20$

Final Answer

The equation of the line in slope-intercept form is: $y = -3x - 20$

Would you like more details on how this was derived, or do you have any questions?

Related Questions:

1. How do you find the slope given two points on a line?
2. How do you convert a line from point-slope to standard form?
3. What does the y-intercept ($b$) represent in a real-world context?
4. How do you verify that a point lies on a given line?
5. Can a line with a slope of zero be expressed in slope-intercept form?

Tip:

To quickly write the equation of a line, remember the point-slope form and understand how to isolate $y$ to achieve the slope-intercept form.