3.4 Standard form

What We Will Learn Graph horizontal and vertical lines Graph standard form using intercepts Story problems

Needed Vocab Standard form: Ax + By = C X- intercept: where graph crosses the x-axis Y-intercept: where graph crosses the y-axis

Ex. 1 Horizontal and Vertical Lines 𝑦=𝑐 C is any number Horizontal line Graph 𝑦=4 𝑥=𝑐 C is any number Vertical line Graph 𝑥=−2

Ex. 2 Using Intercepts to Graph Use when in standard form Ax + By = c Graph 3x + 4y = 12 x-intercept: 3𝑥+4 0 =12 3𝑥=12 3𝑥 3 = 12 3 𝑥=4 y-intercept: 3 0 +4𝑦=12 4𝑦=12 4𝑦 4 = 12 4 𝑦=3 Steps 1. Find x-intercept Plug in 0 for y Plot x-intercept 2. Find y-intercept Plug in 0 for x Plot y-intercept 3. Connect the dots

Your Practice Graph 5𝑥+3𝑦=30 x-intercept: 5𝑥+3 0 =30 5𝑥=30 5𝑥 5 = 30 5 𝑥=6 y-intercept: 5 0 +3𝑦=30 3𝑦=30 3𝑦 3 = 30 3 𝑦=10

Ex. 3 Story Problems You are planning an awards banquet for you school. You need to rent tables to seat 180 people. Tables come in two sizes. Small tables seat 6 people, and large tables seat 10 people. Write an equation and graph the equation. Find four possible combinations. 6𝑥+10𝑦=180 Do same as example 2 6𝑥+10 0 =180 6𝑥=180 6𝑥 6 = 180 6 𝑥=30 6 0 +10𝑦=180 10𝑦=180 10𝑦 10 = 180 10 𝑦=18