Point-slope formula
y - y1 = m(x - x1)
This formula helps to determine the equation of a line given a point (x1, y1) and the slope, m, of the line.
Example 1:
A line contains the point (5, 3) and has a slope of 2. Find the equation of the line.
Step 1:
Identify your point and slope.
(x1, y1) = (5, 3)
m = 2
Step 2:
Substitute and solve for y.
(y - 3) = 2(x - 5) Substitute into formula.
y - 3 = 2x - 10 Distribute.
y - 3 + 3 = 2x - 10 + 3 Add 3 to both sides.
y = 2x - 7 Answer!
Example 2:
Find the equation of the line containing (-4, 6) with a slope of -3.
Step 1:
Identify point and slope.
(x1, y1) = (-4, 6)
m = -3
Step 2:
Substitute and solve for y.
y - 6 = -3(x - -4) Substitute.
y - 6 = -3x - 12 Distribute.
y - 6 + 6 = -3x - 12 + 6 Add 6 to both sides.
y = -3x - 6 Answer
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