Question

On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?

2x + y = 4

2x + y = 8

x + 2y = 4

x + 2y = 8

Answer 1

Parallel lines have the same slope but different y-intercepts

Have you seen the slope intercept form?

y = mx + b

where m is the slope
and b is the y-intercept

Here's an example of two parallel lines

y = 3x + 4
y = 3x - 7

they have the same slope but different y-intercepts

Now obviously your answer choices are in the standard form for a line
Ax + By = C

And all we have to do is rearrange our equation to get to that

so for example, for our earlier equation of y = 3x + 4

-3x + y = 4

We just subtracted 3x on both sides and we were able to make it into the standard form

Answer 2

Now how do we go about solving your question?

Well, first, you have to find the equation for the line that they gave you.

They gave you the slope.

Do you know the slope formula?

\(\sf slope = \frac{y_2 - y_1}{x_2 - x_1}\)
where you have two points \( (x_1, y_1)\) and \( (x_2, y_2)\).

Once you have the slope, replace that number with m in
y = mx + b

And then you can take either point. Either \( (x_1, y_1)\) and \( (x_2, y_2)\)

Plug in the x and y values, and solve for b.

And now you should have the equation in the form of y= mx + b once you plug in the values for 'm' and 'b'

Answer 3

Now you want to find a parallel line that goes through (2, 3)

We have the previous equation in the form of y = mx + b

Remember, parallel lines have the same slope but different y-intercepts

So keep the number you got for 'm' but we'll have to calculate the new value for 'b' our y-intercept

So just plug in the point (2, 3) so x=2 and y=3

And solve for b


Now your equation is in slope intercept form, just rearrange it by bringing x to the other side and you should find something that matches your answer choice

Answer 4

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