Which of the following is the standard form of the equation that passes through (3,−5) and has a slope of 2?

Question

1. -2x - y = 11
2. 2x + y = 11
3. 2x - y = 11
4. 2x - y = -11

Answer 1

B = y - mx

= -5 - (2)(3)

= -5 - 6

= -11

y = 2x-11

0 = 2x-11 - y

2x - y = 11

Answer 2

DEFINITION OF STANDARD FORM

Standard form is Ax + By = C

The letters A, B, and C stand for integers (positive and negative whole numbers).

GIVEN:

The point you are given, (3,-5), gives you the values of x and y --> x = 3 and y = -5.

You are also given the slope. The slope is 2. --> b = 2

IDENTIFY YOUR STARTING POINT

The easiest place to start is to use what you are given. Since we have the x, y, and b values, the easiest form to put it into is slope-intercept form: y = mx + b

So...

y = mx + b plug in what you are given!

-5 = 2(3) + b --> Solve for b!

-5 = 6 + b

-11 = b

Plug b back in to get the slope-intercept form

y = mx + b

y = 2x - 11

PUT IT INTO THE CORRECT FORMAT

Change slope intercept form to standard form. To do this, the x and y values need to be on the same side.

y = 2x -11 --> subtract 2x from both sides

-2x + y = -11

CHECK YOUR ANSWER CHOICES

The standard form version is -2x + y = -11 HOWEVER this is not an answer choice. None of the answers have a negative x-value.

MAKE A QUICK ADJUSTMENT

THEREFORE, if you multiply everything by -1

-1(-2x + y = -11) you get 2x - y = 11.

ANSWER

The answer is 2x - y = 11.

Answer 3

only the last two have slope = 2. the first two have slope =-2

the 3rd is correct, as when you plug in (3,-5) you get 2(3) -(-5) = 6 +5 = 11