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What is the equation of the line that passes through (0,-3) and (2, 2)?

User IamBatman
by
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1 Answer

5 votes

Answer:


y = (5)/(2)x -3

Explanation:

Given points (0,-3) (2, 2), we can start by solving for the slope of the line by using the formula:


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

Let (x1, y1) = (0,-3)

(x2, y2) = (2, 2)

Plug in these values into the slope formula:


m = (y2 - y1)/(x2 - x1) = (2 - (-3))/(2 - 0) = (5)/(2)

Therfore, the slope of the line is
(5)/(2).

Next, we must determine the y-intercept of the line. By definition, the y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

Using the slope (m) =
(5)/(2) and one of the given points, (2, 2), plug in these values into the slope-intercept form, y = mx + b:

y = mx + b


y = (5)/(2)x + b


2 = (5)/(2)(2) + b

2 = 5 + b

Subtract 5 on both sides of the equation to solve for b:

2 - 5 = 5 + b - 5

-3 = b

The y-intercept (b) = -3.

Therefore, the equation of the line that passes through (0,-3) and (2, 2) is:


y = (5)/(2)x -3.

User Tibtof
by
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