Solving Systems by Graphing_AO

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

How do you graph a linear equation?

Back

To graph a linear equation, convert it to slope-intercept form (y = mx + b), identify the slope (m) and y-intercept (b), and plot the y-intercept on the graph. Then use the slope to find another point.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope = rising, negative slope = falling).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot both equations on the same graph and identify the point(s) where they intersect. This point is the solution to the system.

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines in a system of equations indicate that there is no solution, as the lines never intersect.

Front

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

Back

If two lines intersect at one point, it means that there is exactly one solution to the system of equations, which is the coordinates of the intersection point.

Front

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

Back

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

Front

How do you convert standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What is the formula for calculating the slope between two points?

Back

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).