Warm Up Tuesday 11/9/10 We will graph linear equations using intercepts. Simplify each expression:

Warm Up Wednesday 11/10/10 We will graph linear equations using intercepts. Solve each equation:

Today’s Objective To be able to find the x and y intercepts of an equation and use them to draw a quick graph.

The intercepts are where the line crosses the axis. y-Intercept = 6 y x-Intercept = 2 x

Intercepts: Find the x and y intercepts then graph the line y intercept x = 0 Substitute 0 in for x then solve for y x intercept y = 0 Substitute 0 in for y then solve for x

Graph of equation Next graph the x intercept x = -5 at the point (-5,0) First graph the y intercept y = -4 at the point (0,-4) Finally connect the points to form a line

Intercepts: Find the x and y intercepts then graph the line y intercept x = 0 Substitute 0 in for x then solve for y x intercept y = 0 Substitute 0 in for y then solve for x

Graph of equation Next graph the x intercept x = 12 at the point (12,0) (change scale count by 2s) First graph the y intercept y = -8 at the point (0,-8) Finally connect the points to form a line

Compare the 2 graphs

Find the intercepts and graph 3x + 4y = 12

Finding the x-intercept 3x + 4y = 12 3x + 4(0) = 12 3x + 0 = 12 3x = 12 x = 4

Finding the y-intercept 3x + 4y = 12 3(0) + 4y = 12 0 + 4y = 12 4y = 12 y = 3

The graph of 3x + 4y = 12 y y-intercept = 3 x-intercept = 4 x

Find the intercepts and graph y = 4x - 4 You try this one.

Finding the x-intercept y = 4x - 4 0 = 4x - 4 0 + 4 = 4x -4 + 4 4 = 4x 1 = x

Finding the y-intercept y = 4x - 4 y = 4(0) - 4 y = -4

The graph of y = 4x - 4 y x-intercept = 1 x y-intercept = -4

What is the x-intercept of 3x – 4y = 24? (3, 0) (8, 0) (0, -4) (0, -6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of -x + 2y = 8? (-1, 0) (-8, 0) (0, 2) (0, 4) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of x = 3? (3, 0) (-3, 0) (0, 3) None 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Word Problem You make and sell decorative bows. You sell small bows for $3 and large bows for $5. You want to earn $60 per week. This situation can be modeled by 3x + 5y = 60 where x is the number of small bows and y is the number of large bows. Find the intercepts of the graph. Graph the equation Give 3 possible solutions

Finding the y-intercept 3x + 5y = 60 3(0) + 5y = 60 5y = 60 y = 12 (0, 12)

Finding the x-intercept 3x + 5y = 60 3x + 5(0) = 60 3x = 60 x = 20 (20, 0)

Graph of the Equation Large Bows Sold Small Bows Sold

Three Possible Solutions 0 small, 12 large Large Bows Sold 10 small, 6 large 20 small, 0 large Small Bows Sold

Word Problem Your debt d (in dollars) is given by the function: You borrow $1800 from your parents. To repay your debt, you give them $150 per month. Your debt d (in dollars) is given by the function: d = 150t -1800 where t represents time in (months) Find the intercepts of the graph of the function and state what they represent. Graph the equation and identify its domain and range.

Finding the t-intercept d = 150t - 1800 Set d = 0 0 = 150t – 1800 1800 = 150t 12 = t In 12 months the debt = 0

Finding the d-intercept d = 150t - 1800 Set t = 0 d = 150(0) - 1800 d = - 1800 The debt is -$1800 when time is 0.

Graph the function d = 150t -1800 Put time (t) on the x axis Put debt (d) on the y axis

Graph of the function d = 150t -1800 time (t) in months (12, 0) debt (d) in dollars

Identify the domain and range  time (t) in months Range: debt (d) in dollars

Guided Practice Pgs. 225 – 228 Examples 1 – 5