Solving Systems by Graphing

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If m=3 and b=6, what is the slope-intercept equation?

Back

y = 3x + 6

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 5?

Back

(2, 5)

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 first step in solving a system by graphing?

Back

Write both linear equations in slope-intercept form.

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines intersect at a point when graphing a system of equations?

Back

It means there is one unique solution to the system, represented by the coordinates of the intersection point.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of the line represented by the equation y = -2x + 4?

Back

The y-intercept is 4.

Front

What is the slope of the line represented by the equation y = 5x - 3?

Back

The slope is 5.