Equations Tables and Graphs

These are all connected to each other. They all show the same information but in different forms Equation y = 6x + 8 Table x y Ordered pair (x,y) Graph Slope

x y Straight Lines When given an equation and told to plot a graph, first find coordinates of points on the line, this is done by completing a table. By substituting the given values for x calculate the y value for the following equation: y = x This generates coordinates to plot on a graph (-3,-1) (-2,0) (-1, 1) (0, 2) (1, 3) (2, 4) (3, 5)

Straight Lines (-3,-1) (-2,0) (-1, 1) (0, 2) (1, 3) (2, 4) (3, 5) x y Plotting these points x x x x x x x x We find a straight line

Straight Lines Copy and complete this table for the following equation and plot the straight line y = 3x x y x y x x x x x

Straight Lines x y Complete the table for the equation y = x x y x y x y x y Complete the table for the equation y = x - 2 Complete the table for the equation y = x + 3 Complete the table for the equation y = x +1 Plot the coordinates When the table is completed Worksheet 1

What do I do if I don’t have the points given to me??? x y y = 2x + 2

Graphing Step 1: ~ Five Point Method ~ Choose 5 values for x

Graphing Step 2: Find solutions using table y = x + 3 Y | X 0 1 2

Graphing Step 3: Graph the points from the table (0,3) (1,4) (2,5)

Graphing Step 4: Draw a line to connect them

Linear Equations: Equation of a straight line Standard form is AX + BY = C

Slope-Intercept y = mx + b m = slope b = y-intercept

Slope Describes the steepness of a line or rate of change

Y-intercept Where the line crosses the y-axis

Y-intercept The y-intercept has an x-coordinate of ZERO

Y-intercept To find the y- intercept, plug in ZERO for x and solve

X-intercept Where the line crosses the x-axis

X-intercept The x-intercept has a y coordinate of ZERO

X-intercept To find the x- intercept, plug in ZERO for y and solve

Try These Graph using a table (5 point method) 1) y = x + 3 2) y = x - 4

X Y Equation:

A phone company charges $17.50 per month and 12 c for each additional minute. Write a linear equation for the charge in terms of the number of minutes. Let C = charge in dollars Let m = # of minutes C = m ChangeStart Value

This chart shows the price of sliced fruit platters. 1) How much would a 6 lb. platter cost? 1.50 $ = $ ) Write an equation for the cost of a platter that weighs w lbs. Let p = price of platter p = 1.50 w ) How much would a 10 lb. platter cost? p = 1.50 w p = 1.50 ( 10 ) p = = $15.60 ChangeStart Value

Y = 0.75X + 3 You are visiting Baltimore, MD, and a taxi company charges the flat fee of $3.00 for using the taxi and an additional &0.75 per mile. Write an equation that you could use to find the cost of a taxi ride in Baltimore, MD. Let X represent the number of miles and Y represent the total cost.

Kim and Cyndi are starting a business tutoring students in math. They rent an office for $100 per week and charge $40 per hour per student. If they have 15 students each for one hour per week how much profit do they make together in a week? Write and equation.

Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, L, after d days. In how many days will the water level be 26 feet?