Equations, Tables, and Graphs Note Organizer PDF

## Equations, Tables, and Graphs NOTE ORGANIZER Name: A **solution** to an equation with two variables is **true** any **ordered pair** that makes the equation _. **EXAMPLE 1:** Is (2, 6) a solution to the equation y = 3x ? x y 6 = 3(2) 6 = 6√ **yes** **EXAMPLE 2:** For the equation y = 5x - 3...

## Equations, Tables, and Graphs NOTE ORGANIZER Name: A **solution** to an equation with two variables is **true** any **ordered pair** that makes the equation _. **EXAMPLE 1:** Is (2, 6) a solution to the equation y = 3x ? x y 6 = 3(2) 6 = 6√ **yes** **EXAMPLE 2:** For the equation y = 5x - 3, find the missing coordinate: (-4, -23) y = 5(-4) - 3 y = -20 - 3 y = -23 x **EXAMPLE 3:** For the equation y = 2x + 1, find the missing coordinate: (2, 5) _5 = 2x + 1 y _5 - 1 = 2x + 1 - 1 4 = 2x 2 = x y **CLASS TRY:** * **a)** Is (2, 1) a solution to the equation y = 3x - 5? x y 1 = 3(2) - 5 1 = 6 - 5 1 = 1 **yes** * **b)** Is (-2, 1) a solution to the equation y = 3x - 5? x y 1 = 3(-2) - 5 1 = -6 - 5 1 = -11 **no** * **c)** For the equation y = -2x + 3, find the missing coordinate: (-2, 7) -7 = -2x + 3 -7 - 3 = -2x + 3 - 3 -10 = -2x 5 = x y * **d)** For the equation y = -5x - 7, find the missing coordinate: (-3, 8) y = -5(-3) - 7 y = 15 - 7 y = 8 x *** An equation with two variables has **infinitely many** solutions. You can show the solutions by **graphing** them on a coordinate plane. If all of the solutions form a **straight line** when you graph them, then the equation is called a **linear** equation. **Using a table of values to graph the solutions to a linear equation** **EXAMPLE 1:** Graph the equation y = 2x - 2 **Step 1:** Show work: Make a table x y -2 -6 -1 -4 0 -2 1 0 2 2 y = 2x - 2 y = 2(-2) - 2 → y = -6 y = 2(-1) - 2 → y = -4 y = 2(0) - 2 → y = -2 y = 2(1) - 2 → y = 0 y = 2(2) - 2 → y = 2 **Step 2:** Graph the ordered pairs from your table [Graphical representation of plotted points, similar to a coordinate plain, should be shown here] **Step 3:** Use a straightedge to draw a line through the plotted points. (Draw arrows on both ends to show that the line continues in both directions.) *** Use the tables & coordinate grids provided to complete examples #2-5. * **2) y = x + 1** ``` x y -4|-1 -2| 0 0| 1 2| 3 4| 5 ``` Show work: y = (-4) + 1 → y = -1 y = (-2) + 1 → y = 0 y = (0) + 1 → y = 1 [Graphical representation of the equation plotted on a coordinate plain, similar to the one in the provided document] * **3) y = -2x** ``` x y -2| 4 -1| 2 0| 0 1| -2 2| -4 ``` Show work: y = -2(-2) → y = 4 y = -2(-1) → y = 2 y = -2(0) → y = 0 [Graphical representation of the equation plotted on a coordinate plain, similar to the one in the provided document] * **4) y = x + 1** ``` x y -2|-1 -1| 0 0| 1 1| 2 2| 3 ``` Show work: y = -2 + 1 → y = -1 y = -1 + 1 → y = 0 y = 0 + 1 → y = 1 [Graphical representation of the equation plotted on a coordinate plain, similar to the one in the provided document] * **5) y = x - 3** ``` x y -2| -5 -1| -4 0| -3 1| -2 2| -1 ``` Show work: y = -2 - 3 → y = -5 y = -1 - 3 → y = -4 y = 0 - 3 → y = -3 [Graphical representation of the equation plotted on a coordinate plain, similar to the one in the provided document]