4.1b: SIF Given Point and Slope

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 find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated 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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal and does not rise or fall as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where x does not change, resulting in division by zero.

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), then rearrange to slope-intercept form if needed.

Front

Given the point (-2, 5) and slope m = 4, what is the equation of the line?

Back

The equation is y = 4x + 13.

Front

If a line has a slope of -3 and passes through the point (-2, -1), what is the y-intercept?

Back

The y-intercept is b = -7.

Front

What is the y-intercept in the equation y = 5/2x?

Back

The y-intercept is 0, as it can be rewritten as y = 5/2x + 0.