Question

Write the point-slope form of the given line that passes through the points (0, -3) and (4, 1). Identify (x1, y1) as (0, -3). Include your work in your final answer.

(A) y + 3 = x
(B) y = x + 3
(C) y = x - 3
(D) y = -x + 3

Answer 1

To find the point-slope form of the line, calculate the slope using the given points (0, -3) and (4, 1). The slope is 1, and using the point (0, -3), the equation becomes y + 3 = x, which is option (A).

Step-by-step explanation:

To find the point-slope form of the line that passes through the points (0, -3) and (4, 1), we first need to calculate the slope of the line.

The slope (m) is found using the formula m = (y2 - y1) / (x2 - x1). In this case, our points are (0, -3) as (x1, y1) and (4, 1) as (x2, y2). Plugging the values into the formula gives us:

m = (1 - (-3)) / (4 - 0) = (1 + 3) / 4 = 4 / 4 = 1.

Having the slope and using the point (0, -3), we write the point-slope form as:

y - y1 = m(x - x1), which becomes y + 3 = 1(x - 0) or just y + 3 = x.

Therefore, the correct point-slope form is y + 3 = x, making option (A) the correct choice.