Systems: Graphing

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the y-intercept represent in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does the slope of a line indicate?

Back

The slope indicates the steepness of the line and the direction it goes; it is the ratio of the rise (change in y) to the run (change in x).

Tags

CCSS.8.EE.B.5

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines corresponding to the equations, which represent the solutions.

Tags

CCSS.8.EE.C.8B

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you find the point of intersection of two lines graphically?

Back

Plot both lines on the same graph and identify the point where they cross; this point is the solution to the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the x-intercept in a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, represented by the value of x when y = 0.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

Rearrange the equation to solve for y, isolating it on one side to express it in the form y = mx + b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3