Slope from equations

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the rise (change in y) over the run (change in x).

Front

What does the y-intercept represent 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 is 0.

Front

How do you find the slope from the equation y = mx + b?

Back

The slope is represented by 'm' in the equation y = mx + b.

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope is 2.

Front

What is the y-intercept of the equation y = -3x + 4?

Back

The y-intercept is 4.

Front

How can you determine 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 slope of the line represented by the equation y = 0.5x - 2?

Back

The slope is 0.5.

Front

If a line has a slope of 3, what does this indicate about the line's steepness?

Back

A slope of 3 indicates that for every 1 unit the line moves horizontally, it rises 3 units vertically.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 2?

Back

The equation is y = -1x + 2.

Front

What does a slope of 0 indicate about a line?

Back

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