7 1solve By Graphing
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Transcript of 7 1solve By Graphing
Solving Linear Equations UsingGraphingSubstitution
andElimination
Introduction to Unit Six
What’s the Deal?
• There are a number of ways to solve groups of linear equations.
• In this lesson, we will find points on a coordinate plane that solve linear equations in standard form and y-intercept form.
Three Parts(over the next few days)
• Part One – Solve linear equations by graphing.
• Part Two – Solve linear equations by substitution.
• Part Three – Solve linear equations by elimination.
Solving for linear equations answers the question:
• What values of x and y fit into both equations?
• The answer is usually given in (x,y) format (ie. (-4, 6) or (3,8).
Remember - Slope intercept form: y = mx + b
• m = slope• b = y-intercept
• In y = 1/2x – 7, – What is the y-intercept?– What is the slope?
• Rise over Run– Rise = up, or plus one (+1)– Run = right, or plus two (+2).
If the slope is ½
Rise
Run = slope = m
The rise is 1 and the run is 2.
From the origin (0,0), go up 1 and right 2.
Graphing Systems of equations
• y = 3x + 1
• y = -x + 5
• Since both are in y-intercept format (y=mx+b) find the point through which the line intercepts the y-axis.
• Graph these equations. Answers on the next slides.
Graph on the board
Graphy = 3x + 1y = -x + 5
Graphsy = 3x + 1y = -x + 5
Solving By Graphing
Which point or points can fit into both equations?
The result is the ( x,y ) coordinates of the intersection.
The lines inter-cept at (1, 4) sothe solution isx=1, y =4.
The lines inter-cept at (1, 4) sothe solution isx=1, y =4.
The coordinates of the intersecting point is your solution.
Solve by graphing
• y = x +3
• y = x +1
• The next two slides will show the solution.
3
4
2
3
The lines inter-cept at (-20,-12) sothe solution isx= -20, y = -12.
The coordinates of the intersecting point is your solution.
Now solve equations in standard form.
• 3 x + 2y = -6 and
• -3 x + 2y = 6
• Step One: Convert equations from standard form to y-intercept form.
• Let’s review that from a previous lesson using the equations above…
Change 3x + 2y = -6to y-intercept form
3x + 2y = -6
-3x -3x
-2y = -3x - 6
Now we need to get y isolated. In this case, let’s divide both sides by 2.
2y = -3x - 6
2 2 2
Now simplify. y = - x -3
Subtract -3x from both sides
3
2
Change -3x + 2y = 6to y-intercept form
-3x + 2y = +6
+3x 3x
2y = 3x + 6
Get y isolated. Divide both sides by 2.
2y = 3x + 6
2 2 2
Now simplify. y = 3/2x + 3
Add 3x to both sides
Graph the equations:y = -3/2x -3
and y = 3/2x + 3
x = 2, y = 0The solution is(2,0)
Math is NOT a Spectator Sport
Write it Out!
End of Part One
Assignment:pg. 323-4: 10 - 27
Extras for presentation
x y-4-2 0+2+4
-6 -4 -2 0 +2 +4 +6