Three Forms of Linear Equations

Front

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

Back

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

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

The slope is -\frac{2}{3}.

Front

What is the y-intercept of the line represented by the equation 4x - y = 8?

Back

The y-intercept is 8.

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 point-slope form of a linear equation?

Back

The point-slope form is given by y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = \frac{y_2 - y_1}{x_2 - x_1}.

Front

What is the equation of a line with slope 3 that passes through the point (2, 5)?

Back

The equation is y - 5 = 3(x - 2).

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

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope.