Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).A.B.C.D.
Question
Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).
A.
B.
C.
D.
Solution
Step 1: Find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (2, -3) and (x2, y2) = (4, 2).
So, m = (2 - (-3)) / (4 - 2) = 5 / 2 = 2.5
Step 2: Use the point-slope form of the equation of a line, y - y1 = m(x - x1), and substitute m = 2.5, x1 = 2, and y1 = -3.
So, y - (-3) = 2.5(x - 2)
Step 3: Simplify the equation to get it in standard form (Ax + By = C).
y + 3 = 2.5x - 5
Rearrange to get: 2.5x - y = 8
To avoid decimals, we can multiply the entire equation by 2 to get: 5x - 2y = 16
So, the equation of the line in standard form is 5x - 2y = 16.
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