## Which of the following linear equations in standard form contains points (-2,4) and (3,9)?

Question

Which of the following linear equations in standard form contains points (-2,4) and (3,9)?

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1 week 2021-11-26T04:54:56+00:00 2 Answers 0

y=x+6

Step-by-step explanation:

If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.

To find the slope, you should do the change in y over the change in x.

that would be:

(4-9)/(-2-3)

(-5)/(-5)

the slope is 1

plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:

y=mx+b

m=1

y=9

x=3

b=?

9=(1)(3)+b

9=3+b

b=6

The equation of the line would be y=x+6

x – y = – 6

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ – y₁ ) / (x₂ – x₁ )

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (3, 9)

m = = = 1, hence

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 9), then

9 = 3 + c ⇒ c = 9 – 3 = 6

y = x + 6 ← equation in slope- intercept form

Subtract y from both sides

0 = x – y + 6 ( subtract 6 from both sides )

– 6 = x – y, thus

x – y = – 6 ← in standard form