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 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 does it mean if two lines are parallel in terms of their slopes?

Back

If two lines are parallel, they have the same slope but different y-intercepts.

Front

What does it mean if two lines intersect at one point?

Back

If two lines intersect at one point, the system of equations has one unique solution.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation shows two parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The graphical representation shows two lines that overlap completely.

Front

How can you determine the solution to a system of equations by graphing?

Back

The solution is the point where the two lines intersect on the graph.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

What is the relationship between the slopes of two lines that are perpendicular?

Back

The slopes of two perpendicular lines are negative reciprocals of each other, meaning m1 * m2 = -1.

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: y = (-A/B)x + (C/B).