Question

What is an equation of the line that passes through the point (-2, -3) and is

parallel to the line 5x + 2y =14?

Answer 1

The equation of the parallel line will be y = -2.5x - 8.

Explanation:

First things first, let's rearrange the line equation provided into a more standard form:

`5x + 2y = 14`

`5x - 14 = -2y`

`(5x - 14)/(-2) = y`

`y = -2.5x + 7`

Therefore, we can see that this line has a slope (the coefficient preceding x) of -2.5. The parallel line must therefore also have a slope of -2.5.

Now, let us set the y-intercept of the parallel line to be (0, a) (since it must be on the y-axis).

If we factor in all of this, we get the equation:

`(a-(-3))/(0-(-2)) = -2.5`

Remember, the slope is found by dividing the vertical difference with the horizontal difference.

`a - (-3) = -2.5(0+2)`

`a + 3 = -5`

`a = -8`

Hence, the equation of the parallel line will be y = -2.5x - 8.

Hope this helped!