Writing the Equation of a Line SlopeIntercept Form

Slope-Intercept Form The slope-intercept form of a linear equation is y = mx +

Slope-Intercept Form Name the slope and y-intercept of each equation: y = -4 x

Write the equation of a line given. . . 1. 2. 3. 4. 5.

1. Find the Equation of the Line Given the Slope and y-intercept ●Substitute m

2. Find the Equation of a Line Given the Graph • Find the y-intercept

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

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

3. Find the Equation of a Line Given the Point and the Slope ●

Example ● Write the equation of the line with slope = -2 and passing

4. Find the Equation of the Line Given Two Points ● Calculate the slope

Example ● Write the equation of the line that goes through the points (3,

5. Find the Equation of the Line Given the x- and y - intercepts

Example Write the equation of the line with x-intercept 3 and y-intercept 2. x-intercept

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Writing the Equation of a Line

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

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

Write the equation of a line given. . . 1. 2. 3. 4. 5. Slope and y-intercept Graph Slope and one point Two points x - and y-intercepts

1. Find the Equation of the Line Given the Slope and y-intercept ●Substitute m and b into y = mx + b m = -3, b = 1 y = -3 x + 1 m = -2, b = -4 y = -2 x - 4 m = 0, b = 10 y = 0 x + 10, y = 10 m = 1, b = 0 y = 1 x + 0, y = x m = 0, b = 0 y = 0 x + 0, y = 0

2. 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 +2 +3 y x

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

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

3. 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.

4. 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).

5. 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