Solving Systems by Graphing

Front

What are the steps for graphing a line?

Back

1. Plot the y-intercept. 2. Count the slope ratio to plot the second point. 3. Draw the line.

Front

What is the solution to a system of equations when two lines are graphed?

Back

The solution is the point where the two lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two lines to intersect in a system of equations?

Back

It means that there is a unique solution (x, y) that satisfies both equations.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the lines: 1. One solution (lines intersect), 2. No solution (lines are parallel), 3. Infinitely many solutions (lines are the same).

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the y-intercept in graphing a line?

Back

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

Front

How do you find the slope of a line from two points?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Tags

CCSS.8.EE.B.5

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.

Tags

CCSS.8.EE.B.5

Front

If two lines are parallel, what can be said about their slopes?

Back

If two lines are parallel, they have the same slope.

Tags

CCSS.8.EE.B.6

Front

What is the graphical representation of a system with no solution?

Back

The graphical representation is two parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A