Graphing Standard Form Linear Equations

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (x, 0).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, y).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are integers.

Front

How do you find the x-intercept of the equation 2x + y = 6?

Back

Set y = 0 and solve for x: 2x + 0 = 6, so x = 3. The x-intercept is (3, 0).

Front

How do you find the y-intercept of the equation 2x + y = 6?

Back

Set x = 0 and solve for y: 2(0) + y = 6, so y = 6. The y-intercept is (0, 6).

Front

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

Back

The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert the equation x + y = 4 to slope-intercept form.

Back

Rearranging gives y = -x + 4.

Front

What does the slope of a line represent?

Back

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

Front

What is the slope of the line represented by the equation 2x + 4y = 12?

Back

Rearranging to slope-intercept form gives y = -rac{1}{2}x + 3, so the slope is -rac{1}{2}.

Front

What is the significance of the coefficients in the standard form Ax + By = C?

Back

A and B determine the slope of the line, while C represents the point where the line intersects the axes.