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 in Standard Form?

Back

To find the slope (m) from the equation Ax + By = C, rearrange it to slope-intercept form (y = mx + b) and identify the coefficient of x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you find the x-intercept from the equation 4x - 10y = 20?

Back

To find the x-intercept, set y = 0 and solve for x. For the equation 4x - 10(0) = 20, x = 5.

Front

What is the slope of the line represented by the equation 6x + -2y = 18?

Back

The slope of the line is 3, found by rearranging the equation to slope-intercept form.

Front

What does the term 'intercept' refer to in a graph?

Back

An intercept refers to the points where the graph of a function crosses the axes: the x-intercept (where y=0) and the y-intercept (where x=0).

Front

How can you determine the y-intercept from the equation 3x + 4y = 24?

Back

Set x = 0 in the equation to find the y-intercept. For 3(0) + 4y = 24, y = 6, so the y-intercept is (0, 6).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves. A positive slope means the line rises, while a negative slope means it falls.

Front

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

Back

To find the x-intercept, set y = 0. The equation becomes 2x = 35, so x = 17.5, giving the x-intercept (17.5, 0).

Front

How do you convert the equation 7x + 2y = -28 to slope-intercept form?

Back

Rearranging gives y = -rac{7}{2}x - 14, where the slope is -rac{7}{2} and the y-intercept is -14.