**Nowyou t~_ it,** On the graph below, plot and label the following points : A (4, 2), B (-6, -1), C (-5, 6), O (2, -5)

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1 Name Date Period 7 Foundations of Algebra - STUDY GUIDE!!! Your quiz on sections will be..,....so, what will I need to know how to do? Plot points on a coordinate plane (SECTION 4.1) o In an ordered pair, we list the x-coordinate first, and then the y-coordinate second: (x, y). o The x-axis is the horizontal axis (left to right) while the y-axis is the vertical axis (up and down). To plot a point such as (6, -3), you know that the x-coordinate is 6 and the y-coordinate is - 3. Therefore, you would go to the right 6 units, and down 3 units. Your graph would look like this graph to the right O **Nowyou t~_ it,** On the graph below, plot and label the following points : A (4, 2), B (-6, -1), C (-5, 6), O (2, -5) g (6, -3), x and D and record them below. Determine the quadrant in which an ordered pair lies (SECTION 4.1) o Remember that you can help determine which quadrant is which by drawing a big C on a coordinate plane.., like the one below. Where the C starts, quadrant I (1) begins. Where the C ends, you have the last quadrant, or quadrant IV (4). o **Nowyou t~_ R.*~Determine the quadrants of points A, B, C, A- B- C- D- Can you determine the quadrants of the following points: A (-3, 5) and B (5, -3)? (Hint: Plot the points on a coordinate plane if you need to!)

2 Check to see whether an ordered pair (x, y) is a solution of a linear equation o When you are given a linear equation, you should be able to substitute values for variables and check to see if the end result is a true or a false statement. If the result is a true statement (ex: 5=5, -3=-3)... * The point is a solution and * The point lies on the given line. If the result is a false statement (ex: 0=2,-4=4) [] The point is NOT a solution an ~d J The point does NOTlie on the given line Example: Check to see if (2, -9) is a solution to the equationy = 4x 1. Refer to work shown --) -) Determine whether the following points are solutions of the equation 2x - 3y = 8. x,y -9 = 4(2) + 1-9:8+1 o9~9 ~Not a solulion, *Not a point on the line. A (7, 2) (-2,-3) C (10, 4) Write a linear equation in function notation (SECTION 4.2) o O Hm! This is a complicated way of saying... ISOLATE Y!!! All you have to do is solve the equation for y. Remember, think about what is being done to y, and perform the inverse operations in the reverse order to solve for y. -3,~= 1~2-6x ~4 [~olice how each piece of [ [ the equationis~ y = x

3 o **Nowyou t~_ it** Write the following linear equations in function notation. y+2x=9 2x+4y=-6 1/4y- x = 3 Graph a linear equation using a table of values (SECTION 4.2) X 2x+y=-3 Y (x, y) Remember...there are 3 things we need to do here. 1) lsolate y by writing the equation injunction notation. 2) Create a table of values. Lonk at the table ofva nes below. Whenever you create a table of values, it should look like the one below. You would fill in the equation in the y = column, and show your work for each x-value (input). Your result would be a y-value (output). To get your (x, y) pair, iust copy your x and y values!!! 3) Create a line out of plotted ordered pairs! o **Nowyou try it** Graph this linear equation using a table of values: 2x + y = -3. Use the workspace below for step 1. You may use the table above for step 2 and the coordinate plane to the right for step 3! -> -> STEP 1: 2x+y=-3

4 Graph equations of horizontal and vertical lines (SECTION 4.3) o All horizontal lines will begin with y = and oil verti ol lines will begin with x =. o For example, in the equation x = -4, ask yourself this question 1) Choose 3 ordered pairs that have an x-value of -4. Write them on the line below. Where is x ALWAYS -4? o 2) Now, plot your points and graph the line on the coordinate plane below. y 3) Now you trv it. ~ On the graph below, graph the line y = 7. Make a prediction: will this be a horizontal line or a vertical line? **CIRCLE ONE: horizontal vertical 4) Now ro. h =7!! Y, X

5 Write equations of horizontal and vertical lines (SECTION 4.3) o All horizontal lines will begin with y = and all vertical lines will begin with x =. o If you forget this, choose 3 points on the line, and notice which coordinate is always the same. o Here s an example: 5) THINK: What is the same in each of the 3 ordered pairs on this graph? (1,:: 4): : (8, 4) 6} Now, write the equation of the line: o ~ NOW YOU TRYIT: Write the equation o]:the line shown below. Y EQUATION: Plot x- and y- intercepts (SECTION 4.4)

6 o x- intercepts are points that lie on the x- axis and have a y coordinate of 0. o y- intercepts are points that lie on the y- axis and have an x coordinate of 0. o These points are one way to graph a "quick sketch" of a line... all you have to do is connect the points with a line! O X o 8) NOW YOU TRYIT: On the graph to the left, graph the line that has a y-intercept of 6 and an x-intercept of -3. Finding x- and y- intercepts using a linear equation. o Remember that there are two crucial pieces of information that you MUST KNOW about x- and y- intercepts., At the x-intercept, y = 0 [] At the y-intercept, x = 0 o Example: Let s find the x and y intercepts of the equation 2x - 4 = g. X-INTERCEPT (y=0) 2x-4y = 8 2x-4y = 8 2x - 4(0) = 8 Y-INTERCEPT (x=0) 2(0) - 4y = 8 2x-0=8 0-4y=8 2x = 8-4_Z = x=4 y=-2 NOW YOU TRY IT: o 9 & 10) Find the x- an~d y- intercepts of the equation x + 4y = 12. Y X-INTERCEPT : Y-~NTERCEPT : Now, plot the x- and V- Mtercepts on the rq~ph to the r~qht and qraph the line that connects t~hem.