Find the equation of the line that passes through the following two points:(4, -6) and (6, 3)
Question
Find the equation of the line that passes through the following two points:(4, -6) and (6, 3)
Solution
Step 1: Find the slope (m) of the line. The formula to find the slope between two points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1).
Using the given points (4, -6) and (6, 3), the slope m = (3 - (-6)) / (6 - 4) = 9 / 2 = 4.5
Step 2: Use the point-slope form of a line, which is y - y1 = m(x - x1). You can use either of the given points for (x1, y1). Let's use (4, -6).
Substituting the values into the equation, we get y - (-6) = 4.5(x - 4)
Step 3: Simplify the equation to the slope-intercept form (y = mx + b).
y + 6 = 4.5x - 18
Subtract 6 from both sides to get the final equation of the line:
y = 4.5x - 24
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