Question

Find the standard form for the given points (9,7) and (-7,10).

(A) x - y = 2
(B) x + y = 2
(C) x - y = -2
(D) x + y = -2

Answer 1

The standard form of the equation that passes through the points (9,7) and (-7,10) is 3x + 16y = 139. None of the provided answer choices accurately represent this standard form.

Step-by-step explanation:

To find the standard form of the equation that passes through the points (9,7) and (-7,10), you need to determine the equation of the line that those points satisfy. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

First, let's find the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (9,7) and (-7,10), we get:

m = (10 - 7) / (-7 - 9) = 3 / -16 = -3 / 16

Now, we use point-slope form to create the equation:

y - y1 = m(x - x1)

Let's use the point (9,7):

y - 7 = (-3/16)(x - 9)

Multiply both sides by 16 to avoid fractions:

16(y - 7) = -3(x - 9)

Distribute on both sides:

16y - 112 = -3x + 27

Rearrange to get Ax + By = C:

3x + 16y = 139

The closest answer choice to this equation is (A) x - y = 2, but none of the provided options exactly match the standard form we found. Therefore, the correct standard form is not listed among the given options.