Question

On a coordinate plane, a line goes through (negative 3, negative 3) and (negative 1, 5).
What is the equation of the line parallel to the given line with an x-intercept of 4?

y =
x +

Answer 1

To find the equation of a line that is parallel to the line through the points \((-3, -3)\) and \((-1, 5)\) and has an x-intercept of 4, we need to follow these steps:

1. **Find the slope of the given line.**
The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates of our points:
\[
m = \frac{5 - (-3)}{-1 - (-3)} = \frac{5 + 3}{-1 + 3} = \frac{8}{2} = 4
\]

2. **Write the equation of the parallel line.**
Since parallel lines have the same slope, the slope \(m\) of the parallel line will also be 4. The general linear equation can be written in slope-intercept form as:
\[
y = mx + b
\]
So, for our line:
\[
y = 4x + b
\]

3. **Find the y-intercept \(b\) using the x-intercept.**
The x-intercept occurs where \(y = 0\). We know the x-intercept is at \(x = 4\). We substitute this value into the line's equation to find \(b\):
\[
0 = 4(4) + b
\]
\[
0 = 16 + b
\]
Solving for \(b\) gives:
\[
b = -16
\]

4. **Write the final equation of the line.**
Now, we can write the equation of the line parallel to the given line with the proper y-intercept:
\[
y = 4x - 16
\]

So, the equation of the line is:
\[
y = 4x - 16
\]

Thus, the answer is:
\[
y = 4x - 16
\]