Standard Form

Front

What is Standard Form in mathematics?

Back

Standard Form is a way of writing numbers or equations in a specific format. For linear equations, it is typically written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

Convert the equation 2x + 3y = 6 to slope-intercept form.

Back

y = -2/3x + 2

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do you find the slope from the equation 4x - 2y = 8?

Back

Rearranging to slope-intercept form gives y = 2x - 4, so the slope (m) is 2.

Front

What are x-intercepts and y-intercepts?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

Find the x-intercept of the equation 3x + 4y = 12.

Back

Set y = 0: 3x = 12, so x = 4. The x-intercept is (4, 0).

Front

Find the y-intercept of the equation 5x - 2y = 10.

Back

Set x = 0: -2y = 10, so y = -5. The y-intercept is (0, -5).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of -3, what does this indicate about the line?

Back

A slope of -3 indicates that for every 1 unit increase in x, y decreases by 3 units, showing a downward trend.

Front

Convert the equation 6x + 2y = 12 to standard form.

Back

The standard form is 3x + y = 6.