Question

Which equation represents the line that passes through the points (-1,-2) and (3,10)?

A) y=3x +1
B) y =3x-1
C) y= 4x +2
D) y =4x - 2

Answer 1

The correct option is A. y = 3x + 1.

Step-by-step explanation:

To find the equation of the line that passes through the points (-1,-2) and (3,10), you need to determine the slope (m) and the y-intercept (b) of the line using the slope-intercept form of a line, which is y = mx + b.

The slope (m) is calculated as the change in y divided by the change in x between the two points:

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

Applying the coordinates of the given points:

m = (10 - (-2)) / (3 - (-1))

m = 12 / 4 = 3

Now that we have the slope, we can plug the slope and either of the points into the slope-intercept form to solve for the y-intercept (b). Using point (-1,-2):

-2 = 3(-1) + b

-2 = -3 + b

b = -2 + 3

b = 1

Thus the equation of the line can be written as:

y = 3x + 1

Therefore, the correct answer is A) y = 3x + 1.