Slope and Linear 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'. It is calculated as the change in y (rise) over the change in x (run).

Front

What is the slope formula?

Back

The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

How do you find the slope between two points (3, 4) and (7, 10)?

Back

The slope is m = (10 - 4) / (7 - 3) = 6 / 4 = 3/2.

Front

Is the line represented by the equation y = 2x + 3 proportional?

Back

No, because it has a y-intercept (3) and does not pass through the origin.

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

Find the slope of the line represented by the points (1, 2) and (4, 5).

Back

The slope is m = (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0.

Front

If a line has a slope of 4/5, what does this mean?

Back

This means for every 5 units you move to the right (increase in x), you move up 4 units (increase in y).