Solving for y

Front

What is the simple definition of slope?

Back

Slope is defined as the ratio of the rise (vertical change) to the run (horizontal change) between two points on a line.

Front

How do you solve for y in the equation 10x - 2y = 6?

Back

To solve for y, rearrange the equation to isolate y: 2y = 10x - 6, then y = 5x - 3.

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates that the line is horizontal, meaning there is no vertical change as x changes.

Front

How can you express y in terms of x for the equation 4x + 3y = 9?

Back

To express y in terms of x, rearrange the equation: 3y = 9 - 4x, then y = -4/3x + 3.

Front

What is the slope of the line represented by the equation y = 5x - 3?

Back

The slope of the line is 5.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line rises as it moves from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line falls as it moves from left to right.

Front

How can you determine the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

In slope-intercept form, the slope (m) is the coefficient of x.

Front

What is the slope of the line represented by the equation y = -4/3x + 3?

Back

The slope of the line is -4/3.