The line that passes through $$ (3,5) $$ and is parallel to the line through $$ (3,3) $$ and $$ (-3,-1) $$

Question

UpStudy AI · Accepted Answer

To find the equation of the line that passes through the point $$ (3,5) $$ and is parallel to the line passing through $$ (3,3) $$ and $$ (-3,-1) $$, follow these steps:

### 1. Determine the Slope of the Given Line

First, calculate the slope ($$ m $$) of the line passing through $$ (3,3) $$ and $$ (-3,-1) $$.

$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{-3 - 3} = \frac{-4}{-6} = \frac{2}{3}
$$

### 2. Use the Slope-Point Form

Since parallel lines have the same slope, the slope of the desired line is also $$ \frac{2}{3} $$. Use the point-slope form of a line equation, which is:

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

Plugging in the slope $$ m = \frac{2}{3} $$ and the point $$ (3,5) $$:

$$
y - 5 = \frac{2}{3}(x - 3)
$$

### 3. Simplify the Equation (Optional)

If you prefer the equation in slope-intercept form ($$ y = mx + b $$):

$$
y - 5 = \frac{2}{3}x - 2 \
y = \frac{2}{3}x + 3
$$

### Final Answer

**The equation of the desired line is:**

$$
y - 5 = \frac{2}{3}(x - 3)
$$

Or, equivalently,

$$
y = \frac{2}{3}x + 3
$$
The equation of the line is $$ y = \frac{2}{3}x + 3 $$.

The line that passes through \( (3,5) \) and is parallel to the line through \( (3,3) \) and \( (-3,-1) \)

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions