Question

Write an equation of the line that contains the point (-2, 2) and has a slope of -5.

A) y = -5x + 8
B) y = -5x - 12
C) y = 5x + 12
D) y = 5x - 12

Answer 1

y = -5x - 8 None of the answer options are correct.

Step-by-step explanation:

We'll use the slop-intercept format of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero).

We are told the slope is -5, so we can write:

y = -5x + b

Now we need to find the value of b that will shift the line so that it goes through point (-2,2). To do this, use the given point in the equation we have thus far, and calculate the value of b that results:

y = -5x + b

2 = -5(-2) + b for point (-2,2)

2 = 10 + b

b = -8

The equation is y = -5x - 8.

None of the answer options are correct, for the information provided. See the attached graph as proof the above line meets the problem's requirements.

Perhaps option A, y = -5x + 8 was mistyped?

Answer 2

The correct equation of the line with a slope of -5 and passing through the point (-2, 2) is found using the slope-intercept form (y = mx + b). Substituting the values to find the y-intercept, the correct equation is y = -5x - 8, which corresponds to none of the given options, implying there's an error in the options.

Step-by-step explanation:

To write an equation of the line that contains the point (-2, 2) and has a slope of -5, we will use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. Since we are given the slope (-5) and a point through which the line passes ((-2, 2)), we can find the y-intercept by substituting these values into the equation:

y = mx + b
2 = (-5)(-2) + b
2 = 10 + b
b = 2 - 10
b = -8

Now we can write the final equation using the slope and y-intercept we've found:

y = -5x - 8

Comparing this with the given options, the correct choice is A) y = -5x + 8, as the y-intercept we found is -8, and it is mistakenly positive in option A.