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

Answer:

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

Step-by-step explanation:

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

$5x + 2y = 14$

$5x - 14 = -2y$

$\frac{5x - 14}{-2} = y$

$y = -2.5x + 7$

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:

$\frac{a-(-3)}{0-(-2)} = -2.5$

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!