Question

: Find the slope, and write the standard form of the line that passes through the points (-3, 6) and (3, -6).

a) Slope: -2, Standard Form: 2x + y = 0
b) Slope: 2, Standard Form: 2x - y = 0
c) Slope: -2/3, Standard Form: 3x - 2y = 0
d) Slope: 2/3, Standard Form: 3x + 2y = 0

Answer 1

y = -2x

Step-by-step explanation:

The standard form of the equation of a straight line is y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = zero).

We are given 2 points. We'll use them to find the slope, m. Slope is the Rise/Run of a line. That is, the change in y divided by the change in x between two points.

Set the two points in order of x:

(-3, 6) (3, -6)

Rise = (-6 - 6) = - 12

Run = (3 - (-3)) = 6

Rise/Run = -12/6 or -2

m, the slope, is -2

We can now write y = -2x + b since we have m.

We need to find a value of b that shifts the line until it goes through the two points. We can find that value of b by entering one of the two given points. Lets use (3,-6).

y = -2x + b

-6 = -2*3 + b for (3,-6)

-6 = -6 + b

b = 0

The line that goes through points (-3, 6) and (3, -6) is:

y = -2x + 0 or y = -2x

See the attached graph.

Answer 2

The slope of the line passing through the points (-3, 6) and (3, -6) is -2, and the standard form of the equation of this line is 2x + y = 0. The correct answer is a).

Step-by-step explanation:

Finding the Slope and Standard Form of a Line

To find the slope of the line that passes through two points, (-3, 6) and (3, -6), we can use the slope formula:

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

Plugging in the values from the points gives:

slope (m) = (-6 - 6) / (3 - (-3)) = -12 / 6 = -2

Therefore, the slope is -2.

Next, we write the equation of the line in point-slope form and then convert it to standard form. Starting with the point-slope form (y - y1) = m(x - x1) and using one of the given points (-3, 6), we get:

(y - 6) = -2(x + 3)

Expanding this we get:

y - 6 = -2x - 6

And by rearranging the terms to get the standard form, Ax + By = C, we have:

2x + y = 0

This means the correct answer is a) Slope: -2, Standard Form: 2x + y = 0.