What is an equation of the line that passes through the points $$ (2,2) $$ and $$ (4,8) $$ ? Answer Attempt 1 out of 2

Question

UpStudy AI · Accepted Answer

To find the equation of the line that passes through the points $$ (2, 2) $$ and $$ (4, 8) $$, follow these steps:

### 1. **Find the Slope ($$m$$)**

The slope of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points:

$$
m = \frac{8 - 2}{4 - 2} = \frac{6}{2} = 3
$$

### 2. **Use the Point-Slope Form**

With the slope $$ m = 3 $$ and one of the points (let's use $$ (2, 2) $$), the point-slope form of the equation is:

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

Substituting the known values:

$$
y - 2 = 3(x - 2)
$$

### 3. **Simplify to Slope-Intercept Form ($$y = mx + b$$)**

Expand and solve for $$ y $$:

$$
y - 2 = 3x - 6
$$
$$
y = 3x - 6 + 2
$$
$$
y = 3x - 4
$$

### **Final Equation**

$$
\boxed{y = 3x - 4}
$$

This equation represents the line that passes through the points $$ (2, 2) $$ and $$ (4, 8) $$.
The equation of the line is $$ y = 3x - 4 $$.

What is an equation of the line that passes through the points \( (2,2) \) and \( (4,8) \) ? Answer Attempt 1 out of 2