Standard Form

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the slope of a line in standard form?

Back

The slope (m) can be found using the formula m = -A/B from the standard form Ax + By = C.

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

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, indicating the value of y when x = 0.

Front

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

Back

To convert to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the relationship between the coefficients in standard form and the slope?

Back

The slope of the line is the negative ratio of the coefficients of x and y: m = -A/B.

Front

What is the x-intercept of the equation 4x - 10y = 20?

Back

The x-intercept is 5.

Front

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

Back

The y-intercept is (0, -7).