Slope, graphs and equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line. It is calculated as the change in y (rise) over the change in x (run).

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

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

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 'b' in the slope-intercept form.

Front

How can you determine the equation of a line given its slope and y-intercept?

Back

You can determine the equation of a line using the slope-intercept form: y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis, and it can be found by setting y = 0 in the equation of the line.

Front

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

Back

The equation of the line is y = 2x - 3.

Front

How do you convert the equation of a line from 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.