Solving Systems by Graphing

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, y).

Front

How do you find the solution of a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

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

Back

If two lines are parallel, they have no points of intersection, meaning there is no solution to the system.

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

How do you determine the slope from an equation in slope-intercept form?

Back

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

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3) is the solution.

Front

What is the solution to the system of equations y = 2/3x - 2 and y = -x + 3?

Back

(3, 0) is the solution.

Front

What is the solution to the system of equations y = 1/2x + 2 and y = -3x + 9?

Back

(2, 3) is the solution.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and do not intersect.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.