Question

What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply. y = −x − 1 2x + 5y = −5 y = −x − 3 2x + 5y = −15 y − 1= −(x + 5)

Answer 1

ANSWER

$2x+5y= -5$

EXPLANATION

If the line whose equation we are finding is parallel to the line $2x+5y=10$ then it has the same slope as the slope of this line.

Let us write $2x+5y=10$ in slope intercept form;

$\Rightarrow 5y=-2x+10$

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

The slope of this line is $-\frac{2}{5}$ so the line whose equation we are finding also has slope $-\frac{2}{5}$.

Using the slope intercept form; the equation can be written as

$y=mx +c$

When we substitute the slope we get;

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

Since the line passes through the point, $(-5,1)$, it must satisfy its equation.

This implies that;

$1=-\frac{2}{5}(-5) +c$

$1=2 +c$

$-1=c$

Hence the equation is

$y=-\frac{2}{5}x -1$

Multiplying through by 5 gives

$5y=-2x -5$

Or

$5y+2x= -5$

Answer 2

We will find that the equation for the wanted line is:

y = (-2/5)*x - 1

How to find a parallel line?

A general linear equation can be written as:

y = a*x + b

Such that a is the slope and b is the y-intercept.

We know that two lines are parallel if the lines have the same slope but different y-intercepts.

So, if we want our line to be parallel to 2x + 5y = 10, the line must have the same slope. Rewriting this in the slope-intercept form we get:

y = (10 - 2x)/5

y = (-2/5)*x + 2

Then the slope of our line is (-2/5), we will have something like:

y = (-2/5)*x + b

To find the value of b, we use the fact that (-5, 1) must be on the line, this means that:

1 = (-2/5)*-5 + b

1 = 2 + b

1 - 2 = b

-1 = b

Then the line is:

y = (-2/5)*x - 1

If you want to learn more about linear equations, you can read:

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