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

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

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

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**The intercepts are where the line crosses the axis.**

y-Intercept = 6 y x-Intercept = 2 x

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**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

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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

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**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

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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

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Compare the 2 graphs

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**Find the intercepts and graph**

3x + 4y = 12

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**Finding the x-intercept**

3x + 4y = 12 3x + 4(0) = 12 3x + 0 = 12 3x = 12 x = 4

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**Finding the y-intercept**

3x + 4y = 12 3(0) + 4y = 12 0 + 4y = 12 4y = 12 y = 3

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

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**Find the intercepts and graph**

y = 4x - 4 You try this one.

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**Finding the x-intercept**

y = 4x - 4 0 = 4x - 4 0 + 4 = 4x 4 = 4x 1 = x

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**Finding the y-intercept**

y = 4x - 4 y = 4(0) - 4 y = -4

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

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**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

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**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

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**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

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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

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**Finding the y-intercept**

3x + 5y = 60 3(0) + 5y = 60 5y = 60 y = 12 (0, 12)

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**Finding the x-intercept**

3x + 5y = 60 3x + 5(0) = 60 3x = 60 x = 20 (20, 0)

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Graph of the Equation Large Bows Sold Small Bows Sold

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**Three Possible Solutions**

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

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**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 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.

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**Finding the t-intercept**

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

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**Finding the d-intercept**

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

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**Graph the function d = 150t -1800**

Put time (t) on the x axis Put debt (d) on the y axis

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**Graph of the function d = 150t -1800**

time (t) in months (12, 0) debt (d) in dollars

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**Identify the domain and range **

time (t) in months Range: debt (d) in dollars

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Guided Practice Pgs. 225 – 228 Examples 1 – 5

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Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

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