graphing_9.1.notebook March 15, 2019
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4 Writing the equation of a line in slope intercept form. In order to write an equation in y = mx + b form you will need the slope "m" and the y intercept "b". We will subsitute the values for m and b, and leave x and y as is. Writing the equation of a line when we are given the slope and the y intercept. example: write the equation of the line that has a slope of 4 and intercepts the y axis at 5. Writing the equation of a line when given the slope and a point the line goes through. 4
5 Writing the equation of a line when given two points. 5
6 Writing the equation of a line from a graph 6
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8 Writing a function from a table 8
9 Is the equation a linear equation? We want to be able to determine if a given equation is a linear equation, a linear equation has the form y = mx +b (slope intercept form). If an equation matches this form it is considered linear. We can do this by solving for y (get y by itself) and simplify. ex: Is 6x + 3y = 9 a linear equation? If it is find the slope and the y intercept. (hint solve for y) Try it yourself: is y 4 = 2(x 8) a linear equation? If so, find slope and y intercept. 9
10 Parallel and Perpendicular Lines Parallel Lines two lines that go on forever but do not ever touch. Intersecting Lines lines that cross Perpendicular Lines lines that cross and make a right angle(90 degrees) 10
11 Goal: To write equations for parallel and perpendicular lines Parallel lines two lines that are parallel have the same slope. With this knowledge and what we already know about writing equations of lines we can create an equation for line parallel to a given line. Example:Write the equation for a line parallel to the line y = 2x + 5 that goes through point (0, 6). What do we know? Write the equation parallel to the given line 11
12 Perpendicular Lines Perpendicular lines have negative reciprocal slopes(flipped and opposite signs). Using this information we can write the equation of a line perpendicular to another line. ex: Write the equation of a line perpendicular to the y = 2x + 3 that goes through point (0,2). What do we know? 12
13 Quiz 1. What is the slope of the line that goes through points (0, 4) and (8, 6)? 2. Write the equation for a line has a slope of 3 and goes through point ( 2, 5). 3. Write the equation of a line that goes through points (2,3) and (0,5). 4. Solve for x: 2 + x = 3(x 4) 13
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17 How to graph a line We will now focus on graphing a line from an equation. ex: Graph the equation y 2x = 3 Step 1: Get the equation in slope intercept form (y = mx +b). If it is already in this form you can skip this step. Step 2: Find m and b from the equation, they will be your slope and your y intercepts. Step 3: "b" represents the point where you graph touches the y axis, it has the coordinate (0,b), plot that first. Step 4: use the slope(m) to determine rise over run. Rise means you go up or down, and run means left or right. If rise is positive you go up. If run is positive you go right. Step 5: Connect your dots, write the equation on the line and draw arrows and you're done!!!!try to plot at least 4 points and use a straight edge to connect your line!!! 17
18 ex: Graph the equation y 2x = 3 18
19 There are two special graphs 19
20 3/12/19 Systems of Equations Graphing two or more equations on the same xy coordinate plane and checking to see if and where they cross each other. We will do this in two forms the first will be graphically, we graph and find the point where they intersect. The second will be algebraically which will require us to do some math. Graphically If we want to use a graph to determine where two graphs cross we will need to graph the lines. Make sure both equations are in y=mx + b form and locate the point of intersection! ex: 2x + y = 4 3x + y = 2 Graph the following system of equations and locate their intersection(aka, the solution) 20
21 Solving a system of equations algebraically There will be two ways of solving equations algebraically, the subsitution method and the elimination method. They will get us a solution point that we can then check. Substitution Method we solve each equation for y then set the equations equal to each other to get a value for x. We then plug x into on of the equations to get a y value. 21
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