# Point-slope formula

y - y_{1} = m(x - x_{1})

This formula helps to determine the equation of a line given a point (x_{1}, y_{1}) 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.

(x_{1}, y_{1}) = (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.

(x_{1}, y_{1}) = (-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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