What is the equation of the line that passes through the point $$ (-3,1) $$ and has a slope of -3 ?

Question

UpStudy AI · Accepted Answer

To find the equation of a line with a given slope that passes through a specific point, you can use the **point-slope form** of a linear equation:

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

Where:
- $$ m $$ is the slope of the line.
- $$ (x_1, y_1) $$ is the given point on the line.

**Given:**
- Slope ($$ m $$) = -3
- Point ($$ x_1, y_1 $$) = (-3, 1)

**Step 1: Plug the values into the point-slope form**

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

**Step 2: Distribute the slope on the right side**

$$
y - 1 = -3x - 9
$$

**Step 3: Solve for $$ y $$ to get the slope-intercept form ($$ y = mx + b $$)**

$$
y = -3x - 9 + 1
$$
$$
y = -3x - 8
$$

**Final Equation:**

$$
y = -3x - 8
$$
The equation of the line is $$ y = -3x - 8 $$.

What is the equation of the line that passes through the point \( (-3,1) \) and has a slope of -3 ?