Linear Equations & graphs

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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 or negative).

Front

What is the y-intercept of a linear equation?

Back

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

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope decreases as it moves from left to right, indicating that as x increases, y decreases.

Front

What is the graphical representation of a linear function?

Back

The graphical representation of a linear function is a straight line.

Front

How do you convert the equation y = mx + b to standard form?

Back

To convert y = mx + b to standard form, rearrange it to the form Ax + By = C.

Front

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

Back

The slope-intercept form (y = mx + b) clearly shows the slope (m) and the y-intercept (b), making it easy to graph the equation.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.