Standard to Slope-Intercept

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do 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 by isolating it on one side of the equation.

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, indicating how steep the line is and the direction it goes (positive or negative).

Front

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

Back

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

Front

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

Back

y = -2/3x + 2.

Front

What is the significance of the coefficients in the standard form of a linear equation?

Back

The coefficients A, B, and C in the standard form Ax + By = C indicate the relationship between x and y, with A and B representing the direction and steepness of the line.

Front

How can you identify the slope from the equation 4x - y = 8?

Back

Rearranging to slope-intercept form gives y = 4x - 8, so the slope is 4.

Front

What is the first step in converting the equation 3x + 2y = 12 to slope-intercept form?

Back

The first step is to isolate y by subtracting 3x from both sides: 2y = -3x + 12.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the slope of the line represented by the equation y = -5x + 3?

Back

The slope of the line is -5.