Standard Form to Slope-Intercept 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 and B are not both zero.

Front

What is slope-intercept form?

Back

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

Front

How do you convert 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 in terms of x.

Front

Convert the equation 4x - 3y = 15 into slope-intercept form.

Back

y = (4/3)x - 5

Front

Convert the equation 2x + y = 41 into slope-intercept form.

Back

y = -2x + 41

Front

Convert the equation x + 5y = -25 into slope-intercept form.

Back

y = -⅕x - 5

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

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

Back

y = -x + 3

Front

What is the significance of the coefficients A and B in the standard form?

Back

A and B determine the slope of the line when converted to slope-intercept form.