2.4 Writing the Equation of a Line

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Presentation transcript:

2.4 Writing the Equation of a Line

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

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

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

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

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.

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

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

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

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

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.

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.

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

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.

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