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

EXPLANATION

If the line whose equation we are finding is parallel to the line then it has the same slope as the slope of this line.

Let us write in slope intercept form;

The slope of this line is so the line whose equation we are finding also has slope .

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

When we substitute the slope we get;

Since the line passes through the point, , it must satisfy its equation.

This implies that;

Hence the equation is

Multiplying through by 5 gives

Or

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

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

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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