Forms of a linear equation Slopeintercept Form y

Forms of a linear equation Slope-intercept Form y = mx + b Standard Form Ax + By = C Point-Slope Form y – y 1 = m(x – x 1)

If given the slope and yintercept, use slope-intercept form. Example m = 5, b = 7 5 x + ___ 7 y = ___

(B 8) 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: 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. Slope and y-intercept 2. Graph 3. x - and y-intercepts 4. Slope and Point Two Points

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 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

If given the a point and the 4. Find the Equation of the Line slope, Given the Slope and a Point Use slope-intercept form. Example m = – 2, contains (5, – 8) Step 1 Substitute – 2 for m, 5 for x, and – 8 for y; then simplify to find the value of b. y = mx + b – 8 = – 2(5) + b – 8 = – 10 + b 2=b Step 2 Substitute – 2 for m, and 2 for b. y = – 2 x + 2

5. Find the Equation of the Line If given Giventwo Twopoints, Points First, find the slope using the slope formula. Example contains (5, – 8) and (2, 7) -8 m=7– 2– 5 m = 15 – 3 m = – 5

If given two points, Then use the slope and EITHER point to work like the previous example. y = mx + b m = – 5, contains (5, – 8) and (2, 7) 7 = -5(2) + b 7 = -10 + b b = 17 y = – 5 x + 17

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