Writing & Graphing Equations

Front

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

Back

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

Front

How do you convert the equation 4x + 5y = 20 to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), isolate y: 5y = -4x + 20, then y = -\frac{4}{5}x + 4.

Front

What does a vertical line represent in an equation?

Back

A vertical line is represented by an equation of the form x = a, where 'a' is a constant.

Front

What is the slope of the line represented by the equation y = -1x + 2?

Back

The slope of the line is -1.

Front

What is the y-intercept of the equation y = 3x - 4?

Back

The y-intercept is -4, which is the point (0, -4) on the graph.

Front

How do you find the slope from two points (x_1, y_1) and (x_2, y_2)?

Back

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

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction (positive slope goes up, negative slope goes down).

Front

What does the equation y - 2 = \frac{1}{4}(x - 7) represent?

Back

This is a point-slope form of a line that passes through the point (7, 2) with a slope of \frac{1}{4}.

Front

How can you determine if a line is horizontal?

Back

A horizontal line is represented by an equation of the form y = b, where 'b' is a constant.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.