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 convert the equation -8x + 2y = 4 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: 2y = 8x + 4, then y = 4x + 2.

Front

What is the solution to a system of equations?

Back

The solution is any ordered pair (x, y) that makes both equations true.

Front

How can you determine if a point 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 does it mean for two lines to intersect on a graph?

Back

If two lines intersect, it means they have a common solution, which is the point of intersection.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines corresponding to each equation plotted on the same coordinate plane.

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, indicating the value of y when x = 0.

Front

How do you find the slope of a line given two points?

Back

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

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.