The problem in your image asks you to find the equation of a line using two forms:

1. Point-slope form, given a slope of $m = 3$ and a point $(-3, 1)$.
2. Slope-intercept form, using the point-slope form equation.

Let's first break it down:

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,
• $(x_1, y_1)$ is a point on the line.

In this case, the slope $m = 3$, and the point is $(-3, 1)$. Substituting these values into the point-slope form: $y - 1 = 3(x + 3)$ This is the equation of the line in point-slope form.

Slope-Intercept Form:

To convert this to slope-intercept form $y = mx + b$, simplify the above equation: $y - 1 = 3(x + 3)$ Distribute the 3: $y - 1 = 3x + 9$ Now, add 1 to both sides: $y = 3x + 10$ This is the slope-intercept form of the equation.

Final Answer:

• Point-slope form: $y - 1 = 3(x + 3)$
• Slope-intercept form: $y = 3x + 10$

Would you like a deeper explanation, or do you have any questions about this solution?

Here are some related questions to expand your understanding:

1. How would the equation change if the slope was negative?
2. Can you find the x-intercept of the line?
3. How do you convert from slope-intercept to standard form?
4. What is the significance of the slope in this equation?
5. What would the equation look like if the line passed through a different point?

Tip: In geometry, always check the direction of your slope visually if you are working with a graph to ensure the slope value makes sense for the given line.