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

How do you find the slope from the equation 6x - y = 9?

Back

To find the slope, rearrange the equation into slope-intercept form (y = mx + b). The slope (m) is the coefficient of x. For 6x - y = 9, the slope is 6.

Front

What is the y-intercept of the equation 2x - 5y = 35?

Back

To find the y-intercept, set x = 0. For 2(0) - 5y = 35, solving gives y = -7. Thus, the y-intercept is (0, -7).

Front

How do you find the x- and y-intercepts of the equation x + y = -2?

Back

To find the x-intercept, set y = 0: x + 0 = -2, so x = -2. To find the y-intercept, set x = 0: 0 + y = -2, so y = -2. The intercepts are (-2, 0) and (0, -2).

Front

What are the x- and y-intercepts for the equation 5x - 3y = 15?

Back

To find the x-intercept, set y = 0: 5x = 15, so x = 3. To find the y-intercept, set x = 0: -3y = 15, so y = -5. The intercepts are (3, 0) and (0, -5).

Front

How do you find the x and y intercepts of the equation 4x - 5y = 40?

Back

For the x-intercept, set y = 0: 4x = 40, so x = 10. For the y-intercept, set x = 0: -5y = 40, so y = -8. The intercepts are (10, 0) and (0, -8).

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means it rises, negative slope means it falls).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is zero.

Front

How can you convert an equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y: y = -A/B * x + C/B.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope. This means they will never intersect and are always equidistant from each other.