Linear Equation Review

Front

What is the formula to calculate the slope (m) of a line passing through two points (x1, y1) and (x2, y2)?

Back

m = (y2 - y1) / (x2 - x1)

Front

What does a slope of 1/3 indicate about a line's steepness?

Back

The line rises 1 unit for every 3 units it runs horizontally, indicating a gentle upward slope.

Front

What is the slope of a line that is perpendicular to a line with a slope of 1/2?

Back

The slope of the perpendicular line is -2 (negative reciprocal of 1/2).

Front

Convert the point-slope form equation y - y1 = m(x - x1) to slope-intercept form (y = mx + b).

Back

Rearranging gives y = mx + (y1 - mx1).

Front

What is the slope of a line that passes through the points (0, 5) and (3, 3)?

Back

The slope is -2/3.

Front

Identify the slope-intercept form of the equation y = 3x - 1.

Back

The slope is 3 and the y-intercept is -1.

Front

What is the y-intercept of the line represented by the equation y = 1/4x + 2?

Back

The y-intercept is 2.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.

Front

What is the equation of a line that is perpendicular to y = 2x + 3?

Back

The perpendicular line has a slope of -1/2, so an example equation is y = -1/2x + b.

Front

What does the term 'slope-intercept form' refer to in linear equations?

Back

It refers to the form y = mx + b, where m is the slope and b is the y-intercept.