Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope $$ =4 $$, passing through $$ (-7,8) $$ Type the point-slope form of the equation of the line. (Simplify your answer. Use integers or fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. $$ \square $$ (Use integers or simplified fractions for any numbers in the equation.) (s) possiole ( 1 .

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UpStudy AI · Accepted Answer

To find the equations of the line with a slope of $$ 4 $$ that passes through the point $$ (-7, 8) $$, we'll follow these steps:

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

Given:
- Slope $$ m = 4 $$,
- Point $$ (x_1, y_1) = (-7, 8) $$,

Plugging these values into the point-slope formula:
$$
y - 8 = 4(x - (-7))
$$
Simplify:
$$
y - 8 = 4(x + 7)
$$

**Point-Slope Form:**
$$
y - 8 = 4(x + 7)
$$

---

### 2. Slope-Intercept Form

The **slope-intercept form** of a line is:
$$
y = mx + b
$$
where:
- $$ m $$ is the slope,
- $$ b $$ is the y-intercept.

Starting from the point-slope form:
$$
y - 8 = 4(x + 7)
$$
Distribute the slope $$ 4 $$:
$$
y - 8 = 4x + 28
$$
Add $$ 8 $$ to both sides to solve for $$ y $$:
$$
y = 4x + 36
$$

**Slope-Intercept Form:**
$$
y = 4x + 36
$$

---

**Final Answers:**

- **Point-Slope Form:** $$ y - 8 = 4(x + 7) $$
- **Slope-Intercept Form:** $$ y = 4x + 36 $$
**Point-Slope Form:** $$ y - 8 = 4(x + 7) $$ **Slope-Intercept Form:** $$ y = 4x + 36 $$

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