Question

What is the equation of the line that contains (-2, 6) and (4, -3)?

A) y = 3/4x + 5
B) y = -3/2x + 3
C) y = -3/2x - 3
D) y = -4/3x - 3

Answer 1

B) y = -(3/2)x + 3

Step-by-step explanation:

Lets look for a line equation of the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when is is zero).

The slope is known as the Rise/Run, the change in y over the change in x between two points.

We are given two points. Lets calculate Rise/Run

Going from (-2, 6) to (4, -3):

Rise = (-3 - 6) = - 9

Run = 4 - (-2) = 6

Slope, m = (-9/6) or -(3/2)

We can write y = -(3/2)x + b

We need to find a value of be that will shift eht line to intercept the two given points. To find such a value (b), enter one of the two points into the equation and solve for b:

y = -(3/2)x + b

-3 = -(3/2)*4 + b for (4,-3)

-3 = -6 + b

b = 3

The equation becomes y = -(3/2)x + 3

See the attached graph.

Answer 2

The equation of the line passing through the points (-2, 6) and (4, -3) is y = (3/2)x + 9 when calculated using the slope-intercept form method. However, none of the provided options exactly match this equation, indicating an error in the answer choices.

Step-by-step explanation:

The student is asking for the equation of the line passing through two given points: (-2, 6) and (4, -3). To find the equation of a line in slope-intercept form, which is y = mx + b, we first need to calculate the slope (m). The slope is the change in y divided by the change in x, which would be (6 - (-3))/( -2 - 4). Simplifying this gives us a slope of -9/-6, or 3/2.

Next, we use one of the points to solve for the y-intercept (b). Let's use the point (-2, 6). Plugging in the slope and the point into y = mx + b results in the equation 6 = (3/2)(-2) + b. Simplifying 6 = -3 + b leads to b being 9.

The final equation of the line is y = (3/2)x + 9. Now, we have to check which of the provided options matches our equation. Option B, y = -3/2x + 3, has the correct slope but not the correct y-intercept. Option C, y = -3/2x - 3, has the correct slope but a negative y-intercept. None of the options perfectly match our equation, so it appears there may be a mistake in the provided answer choices.