Writing Equations of Lines

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the steepness of the line, indicating how much y changes for a unit change in x.

Front

If two lines are parallel, what can be said about their slopes?

Back

Parallel lines have the same slope.

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form is given by 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) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in the equation of a line?

Back

The y-intercept (b) is the point where the line crosses the y-axis.

Front

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

Back

Rearranging gives y = mx - mx1 + y1.

Front

What is the equation of a line with slope 3 that passes through the point (2, 5)?

Back

Using point-slope form: y - 5 = 3(x - 2) simplifies to y = 3x - 1.

Front

Identify the slope of the line represented by the equation y + 2 = 4(x - 1).

Back

The slope is 4.

Front

What is the slope of the line represented by the equation y - 1 = -2(x + 3)?

Back

The slope is -2.

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.