Assignment Aline passes through $$ (0,-2) $$ and $$ (4,6) $$ Find the equation of a line parallel to this Nine passing through $$ (-3,-1) $$

Question

UpStudy AI · Accepted Answer

To find the equation of a line parallel to the one passing through the points $$ (0, -2) $$ and $$ (4, 6) $$, and that also passes through the point $$ (-3, -1) $$, follow these steps:

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

First, determine the slope ($$ m $$) of the line passing through $$ (0, -2) $$ and $$ (4, 6) $$.

The slope formula is:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points:
$$
m = \frac{6 - (-2)}{4 - 0} = \frac{8}{4} = 2
$$

So, the slope of the given line is **2**.

### 2. Use the Slope for the Parallel Line

Parallel lines have **the same slope**. Therefore, the parallel line we're seeking also has a slope of **2**.

### 3. Use the Point-Slope Form to Find the Equation

With the slope $$ m = 2 $$ and the point $$ (-3, -1) $$, we can use the point-slope form of a line to find its equation:
$$
y - y_1 = m(x - x_1)
$$
$$
y - (-1) = 2(x - (-3))
$$
$$
y + 1 = 2(x + 3)
$$

### 4. Simplify to Slope-Intercept Form (Optional)

To express the equation in the slope-intercept form ($$ y = mx + b $$):
$$
y + 1 = 2x + 6
$$
$$
y = 2x + 6 - 1
$$
$$
y = 2x + 5
$$

### **Final Answer**

The equation of the line parallel to the one passing through $$ (0, -2) $$ and $$ (4, 6) $$, and that also passes through $$ (-3, -1) $$, is:
$$
y = 2x + 5
$$
The equation of the parallel line is $$ y = 2x + 5 $$.

Assignment
Aline passes through and
Find the equation of a line parallel to this
Nine passing through

Upstudy AI Solution

Answer

Solution

1. Find the Slope of the Given Line

2. Use the Slope for the Parallel Line

3. Use the Point-Slope Form to Find the Equation

4. Simplify to Slope-Intercept Form (Optional)

Final Answer

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Assignment Aline passes through and Find the equation of a line parallel to this Nine passing through