Write these in slope-intercept form
1. 2x+y=3
2. -x+(1\2)y=3
3. x-3y=-6
4. 2y-6=x
1. y=-2x+3
2. y=2x+6
3. y=(1\3)x+2
4. y=(1\2)x+3
Which is the graph of the system of equations y = 3x + 6 and y = 3x +1?
The second graph
The first equation from the system of equations is graphed. Graph the second equation to find the solution of the system of equations.
y = -x,
y = 2x + 6
What is the point of intersection?
(-2, 2)
The blue line is the graph of y = -x + 3. Use the sliders to make the orange line represent y = -2x + 9. Examine the graph. What appears to be the solution of this system of equations?
(6,-3) -3=-3
Rewrite the system of equations in slope-intercept form.
y - 5 = -4x,
3y - 9 = -6x
The slope-intercept form of the first equation is y = -4x + 5y
The slope-intercept form of the second equation is y = -2x + 3y
The blue line is the graph of y = -4x + 5. Use the sliders to make the orange line represent y = -2x + 3. Examine the graph. What is the solution of the system of these two equations?
(1, 1)
Consider the system of equations, x - 2y = 8 and -2x + 4y = -16.
1. What is x - 2y = 8 in slope-intercept form?
2. What is -2x + 4y = -16 in slope-intercept form?
3. How many solutions will there be?
4. What will the graph of the system look like?
1. y= (1/2)x -4
2. y= (1/2)x -4
3. infinitely many solutions
4. the lines are exactly the same
Which graph represents the solution set to this system of equations?
y = -1\2x + 3 and y = 1\2x - 1
The fourth graph
Consider the system of equations.
y = -2x + 4,
3y + x = -3
Which statement is true of this system of equations?
The second equation converted to slope-intercept form is
The first equation from the previous system of equations is graphed. Graph the second equation to find the solution of the system of equations.
y = −2x + 4,
y = − 1\3 x − 1
What is the solution to the system?
(3,-2)
Consider the system of equations.
y = −2x + 4 y = − 1\3 x − 1
The solution is (3, -2).
Verify the solution. Which true statement appears in your check?
-2 = -2
Consider the system of equations.
y = 3x + 2 y = − 2\3 x − 4
Explain why these particular equations can be graphed immediately.
Sample Response: These equations are in slope-intercept form. I can use the y-intercept and slope to graph both lines. I plot the y-intercept and use rise over run to locate another point on the line. Then, I can draw a line through the two points.
Roxanne graphed this system of equations to find the solution.
y = 2\3 x − 5 y = −2x + 3
She determined that the solution is (-3, -3). Is she correct? If not, explain why.
No. She used the wrong slopes when graphing the equations
Which graph represents the solution set to this system of equations?
-x + 2y = 6 and 4x + y = 3
The third graph
The blue line is the graph of y - 1 = x. Use the sliders to make the orange line represent 2x + y = -5. Examine the graph. What is the solution of the system of these two equations? Hint: Convert to slope-intercept form before using the sliders.
The solution to the system is
(-2,-1)
The blue and orange lines represent a system. Use the sliders to manipulate the orange line to determine which equations would create a system that has no solution. Check all that apply. Hint: Convert to slope-intercept form.
2x + y = -5
-2x = y
2x = 4 - y
The graph of the equation y = 12 x + 2 is displayed. Which equations would intersect the orange line at the y-intercept? Check all that apply.
A C D