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**2.4 Writing the Equation of a Line**

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**Review of Slope-Intercept Form**

The slope-intercept form of a linear equation is y = mx + b. m represents the slope b represents the y-intercept

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**Review of Slope-Intercept Form**

Name the slope and y-intercept of each equation: m = -4, b =3 m = , b = 5 Rewrite as y = -8x , m = -8, b = Rewrite as y = 2x - 5, m = 2, b = -5 Rewrite as y = x + 0, m = , b = 0 Rewrite as y = 0x + 5, m = 0, b = 5 y = -4x + 3 y = 5 – x 8x + y = 4x - 2y =10 y = x y = 5

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**Write the equation of a line given...**

1. Slope and y-intercept 2. Graph 3. Slope and one point 4. Two points 5. x - and y-intercepts

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**Find the Equation of the Line Given the Slope and y-intercept**

Substitute m and b into y = mx + b m = -3, b = 1 m = -2, b = -4 m = 0, b = 10 m = 1, b = 0 m = 0, b = 0 y = -3x + 1 y = -2x - 4 y = 0x + 10, y = 10 y = 1x + 0, y = x y = 0x + 0, y = 0

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**Find the Equation of a Line Given the Graph**

Find the y-intercept from the graph. Count the slope from the graph. To write the equation of the line, substitute the slope and y-intercept in the slope-intercept form of the equation.

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Example 1 b = -3 m = y = x - 3 x y +2 +3

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Example 2 b = 1 m = y = x + 1 x y +1 -2

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Example 3 b = 4 m = 0/1= 0 y = 0x + 4, y = 4 x y

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**Find the Equation of a Line Given the Point and the Slope**

Use the Point-Slope Formula: is the given point Substitute m and into the formula

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Example Write the equation of the line with slope = -2 and passing through the point (3, -5). Substitute m and into the Point-Slope Formula.

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**Find the Equation of the Line Given Two Points**

Calculate the slope of the two points. Use one of the points and the slope to substitute into the Point-Slope formula.

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Example Write the equation of the line that goes through the points (3, 2) and (5, 4).

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**Find the Equation of the Line Given the x- and y - intercepts**

Write the intercepts as ordered pairs. The x-intercept 4 is the ordered pair (4, 0). The y-intercept -2 is the ordered pair (0, -2). Calculate the slope. Substitute the slope and the y-intercept (b) into the slope-intercept formula.

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**Example Write the equation of the line with x-intercept 3**

and y-intercept 2. x-intercept 3 = (3, 0); y-intercept 2 = (0, 2) Slope: y = mx + b

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Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

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