Solve linear systems by graphing Warm-up

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

How do you convert the equation 3x + 2y = -6 into slope-intercept form?

Back

y = -3/2 x - 3

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept of a line in slope-intercept form?

Back

The y-intercept is the value of y when x = 0, represented as 'b' in the equation y = mx + b.

Front

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

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

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

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect and have no solution.

Front

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

Back

Perpendicular lines intersect at a right angle and have slopes that are negative reciprocals of each other.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 in the equation and solve for x.

Front

What is the significance of the point (1, -1) in a linear system?

Back

It is a solution to the system, meaning it satisfies both equations.