Math Graphing Linear Equations and Graphing Linear Inequalities

Any line parallel to the x-axis is_____ what type of slope would that be? Any line parallel to the y-axis is_____ What type of slope would that be?

parallel to x=horizontal so it has *zero* slope parallel to y=vertical so it has an *undefined* slope

How do you find the x and y intercepts in an equation?

(If confusing look at the bottom of page 2 in the linear equations packet) y=-2x+6 write x-int on one side and y-int on the other. put y=0 of x-int side and x=0 on the y-int side write the equation in the x-int side but fill y in with 0 and solve. write the equation on the y-int side and fill x in for 0 and solve the answer is put in ( , ) for y=-2x+6 the answer on the x-int side is (3,0) and the answer is (0,6) on the y-int side try 3y=-4x-9 on the bottom of page 2 in the linear equation packet

What are the steps for graphing an equation?

1. Get in y=mx+b form 2. solve for y and say what m and b are 3. plot the y-int or b on the graph 4. plot at least 3 points for slope (m=rise over run) 5. connect dots with ruler Try solving -3-y/2=x on first page of linear function packet

name the types of slope: 1. <----> straight horizontal 2. diagonal starting low left to high right (goes up) 3 diagonal starting high left to low right (goes down) 4. vertical line

1. zero slope 2. Positive slope (number positive) 3. negative slope (number negative) 4. undefined or no slope (NOT when slope is zero) 0 over X is 0 so that is zero slope (type in calculator and get 0) X over 0 is undefined because when you type it in your calculator it says error

m=3/4 is this the answer or should you use a decimal?

3/4 is the answer because you always simplify the fraction and you never divide it making a decimal

Parallel lines and Perpendicular lines

Parallel line: -never intersect -always the same distance apart *-the slopes will always be equal* Perpendicular line: -lines that intersect and form a right angle (90 degrees) -product of their slopes is -1 *-Slopes and negative reciprocals of each other* Try these on back of linear equations packet -3x-y=4 and 6x+2y=10 4y=2x-8 and y=-1/2x

When graphing what do you need?

Straight edge mark y and x-axis arrows at end of *ALL* lines *right the equation on the line you graph*

What is the slope intercept form in an equation for a line?

To graph and slove the equation must be in y=mx+b form try solving 1/2x+3/4=1/3y on page 3 of linear equations packet. Or try 2x+3y=6 *If nothing is written for b its 0 and if there is just an x for mx its really 1* order matters for this y is first then = then mx or just x then b (can be + or -)

How do you find the slope between 2 pairs? A(-4,5) and B(3,-2) Try solving J(-2,5) and K(-2,4) answer is on first page of linear equations packet

Use the equation m=y2-y1 over x2-x1 For the points shown in the question -4 is x1, 5 is y1, 3 is x2, and -2 is y2 ^fill in for the formula at the top For your answer you should never have a mixed number or a decimal for anything

Draw a line with m=2 that passes through (-2,3) Graph it to find the y-int and make an equation

bottom on first page of linear equation

If you are given a slope and a point that the line must pass through, how do you plot the line? Try (-2,3) and m=-5/3

the slope will be what comes after m= and the point in must pass through is in the ( , ) plot the given point and use the given slope to continue the line. If the slope is a whole number make it a fraction by putting a 1 at the bottom of the fraction. If it is negative only the top number is negative, if its positive keep it positive. start with the top number, go up the amount it is if its positive but if its negative go down from the marked point. Next take the bottom number and go left if its negative and right if its positive and than plot the next point there. For this specific equation the bottom number will not be negative nut for others it may be negative. For practice plot (-2, 3) and m=-5/3 The answer is on the second page of the linear equations packet. (-5/3 is a fraction)

What is the x-int (intercept) and the y-int? What is the value of y for the point that the line hits the x-axis and what is the value of x when the line hits the y-axis?

x-int is where the line intersects the x-axis y-int is where the line intersects the y-axis x-int:Where the line crosses the x-axis the y=0 y-int:Where the line crosses the y-axis the x=0

y=4 horizontal or vertical? x=4 horizontal or vertical?

y=4 plotted on y axis and horizontal x=4 plotted on x axis and vertical plot y=-8 and x=4