Solving Systems of Equations by Graphing (y=mx+b form)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the slope-intercept form of a line look like?

Back

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the slope (m) from an equation in slope-intercept form?

Back

The slope (m) is the coefficient of x in the equation y = mx + b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you graph the equation y = mx + b?

Back

1. Start at the y-intercept (0, b). 2. Use the slope (rise/run) to find another point. 3. Draw a line through the points.

Front

What is the solution to a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

If two lines are parallel, they have the same slope but different y-intercepts, meaning they have no solution.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are coincident when graphing a system of equations?

Back

If two lines are coincident, they lie on top of each other, meaning they have infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

1. One solution: lines intersect at one point. 2. No solution: lines are parallel. 3. Infinitely many solutions: lines are coincident.

Tags

CCSS.8.EE.C.8A

Front

Solve the system of equations by graphing: y = -2/3x + 4 and y = -1/3x + 1.

Back

The solution is (9, -2).

Tags

CCSS.8.EE.C.8B