2.3 Quick Graphs of Linear Equations Algebra 2

Slope-Intercept Form Slope intercept form: y=mx+b m=slope b=y-intercept (where the graph intersects the y-axis)

Graphing Equations in Slope-Intercept Form Write the equation in slope-intercept form Graph the y-intercept Use slope to “rise and run” to another point Draw a line through the points

Example Graph 𝑦= 1 2 𝑥+1

Example To buy a $1200 stereo, you pay a $200 deposit and then make weekly payments according to the equation 𝑎=1000−40𝑡, where a is the amount you owe and t is the number of weeks. How much do you owe originally? What is your weekly payment? Graph the model.

example The number of gallons g of water in your storage tank is given by 𝑔=500−20𝑡, with t in days. Using a graph, find the daily rate of water use, and determine in home many days the tank will become empty.

Standard Form Standard form: Ax + By = C ; where A and B are not zero x-intercept: where the line intersects the x-axis

Graphing Equations in Standard Form Write the equation in standard form Find the x-intercept by making y=0 and solving for x. Graph the x-intercept. Find the y-intercept by making x=0 and solving for y. Graph the y-intercept. Draw a line through the points

Examples Graph 3𝑥−2𝑦=6 using standard form. Then rewrite the equation in slope-intercept form. Graph 2𝑥+5𝑦=10 using standard form.

Horizontal and Vertical Lines Horizontal Lines: The graph of 𝑦=𝑐 is a horizontal line through (0, c) Vertical Lines: The graph of 𝑥=𝑐 is a vertical line through (c, 0)

Example Graph the following equations 𝑦=−2 𝑥=3 𝑦=1 𝑥=−1

Example Students are selling tickets to a school play. The goal is to raise $600. Tickets are $4 for adults and $3 for students. Describe the numbers of adult and student tickets sold that will reach the goal.

Example If x represents the number of 4 in high bricks and y is the number of 6 in bricks it takes to reach the top of a 60 in wall, what are the endpoint of the segment containing the numbers of 4 in and 6in bricks that will reach the top?