Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation Slope $$ =5 $$, passing through $$ (7,4) $$

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Certainly! Let's work through the problem step by step.

### **Given:**
- **Slope (m):** 5
- **Point (x₁, y₁):** (7, 4)

### **1. Point-Slope Form**

The **point-slope form** of a linear equation is useful when you know the slope of the line and a point that lies on the line. The formula is:

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

**Plugging in the given values:**
- $$ m = 5 $$
- $$ x_1 = 7 $$
- $$ y_1 = 4 $$

$$
y - 4 = 5(x - 7)
$$

This is the **point-slope form** of the equation for the line.

### **2. Converting to Slope-Intercept Form**

The **slope-intercept form** is another way to express a linear equation, and it is given by:

$$
y = mx + b
$$

where:
- $$ m $$ is the slope
- $$ b $$ is the y-intercept

Let's convert the point-slope form we found into slope-intercept form.

**Starting with the point-slope form:**
$$
y - 4 = 5(x - 7)
$$

**Step-by-Step Conversion:**
1. **Distribute the slope (5) on the right-hand side:**
   $$
   y - 4 = 5x - 35
   $$
2. **Add 4 to both sides to solve for $$ y $$:**
   $$
   y = 5x - 35 + 4
   $$
3. **Combine like terms:**
   $$
   y = 5x - 31
   $$

Now, the equation is in **slope-intercept form**:
$$
y = 5x - 31
$$

### **Summary:**
- **Point-Slope Form:** $$ y - 4 = 5(x - 7) $$
- **Slope-Intercept Form:** $$ y = 5x - 31 $$
The point-slope form of the equation is $$ y - 4 = 5(x - 7) $$, and the slope-intercept form is $$ y = 5x - 31 $$.

Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation Slope \( =5 \), passing through \( (7,4) \)

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