4.13: Systems by Graphing

Front

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

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

One solution occurs when lines intersect at one point, no solution occurs when lines are parallel, and infinitely many solutions occur when lines are the same.

Front

What is the slope of the line represented by the equation y = -3/2x + 4?

Back

The slope of the line is -3/2.

Front

What is the solution to the system of equations represented by the lines y = 4x + 3 and y = -1x + 3?

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.

Front

What does the term 'system of equations' refer to?

Back

A system of equations is a set of two or more equations with the same variables.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it on the graph, use the slope to find another point, and draw a line through the points.