Solving Systems by graphing

Front

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

Back

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

Front

How do you identify the slope in the equation y = mx + b?

Back

The slope is represented by the coefficient m in the equation.

Front

What does the y-intercept represent in the slope-intercept form?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

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

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that the system has no solution.

Front

How can you determine if a point (x,y) is a solution to a system of equations?

Back

A point (x,y) is a solution if it satisfies both equations in the system.

Front

What is the graphical representation of a system of equations with one solution?

Back

The graphical representation shows two lines intersecting at a single point.

Front

What is the solution to a system of equations represented graphically?

Back

The solution is the point where the two lines intersect.

Front

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

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What does it indicate if a system of equations has infinitely many solutions?

Back

It indicates that the two equations represent the same line, meaning they overlap completely.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients determine the slope and the position of the line in the coordinate plane.