Question

Using the following points, create an equation in point-slope form.

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

Answer 1

The equation in point-slope form among the given options is A) y - 3 = 2(x - 1).

Step-by-step explanation:

The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line, and m is the slope of the line. Among the provided options, option A fits the point-slope form equation format. Here, the equation y - 3 = 2(x - 1) corresponds to a line with a slope of 2 and passing through the point (1, 3). This form allows for a direct identification of the slope and a point on the line, adhering to the point-slope equation format.

The equation is presented as y - 3 = 2(x - 1), indicating that the line has a slope of 2 and passes through the point (1, 3). By comparing this equation format to the standard point-slope form, it's evident that the constants (-3 and 1) correlate with the y-coordinate and x-coordinate of the point on the line, respectively. The coefficient of (x - 1), which is 2, represents the slope of the line. Therefore, option A correctly represents the equation in point-slope form among the provided choices.