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 expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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

What is slope-intercept form?

Back

Slope-intercept form is a way of writing the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

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

Front

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

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

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

Back

y = -rac{2}{3}x + 2.

Front

Convert the equation 4x - 2y = 8 into slope-intercept form.

Back

y = 2x - 4.

Front

What is the slope of the line represented by the equation 5x + 2y = 10?

Back

The slope is -rac{5}{2}.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, y increases by 3 units.

Front

What is the first step in graphing a linear equation in standard form?

Back

The first step is to convert the equation into slope-intercept form (y = mx + b) to easily identify the slope and y-intercept.