Standard Form and Intercepts

Front

What is the standard form of a linear equation?

Back

Ax + By = C

Front

What is the y-intercept of a line?

Back

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

Front

How do you find the y-intercept from the equation 3x - 4y = -24?

Back

Set x = 0 and solve for y, resulting in (0, 6).

Front

How do you find the x-intercept from the equation 3x - 4y = -24?

Back

Set y = 0 and solve for x, resulting in (-8, 0).

Front

What does the x-intercept represent?

Back

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

Front

What is the significance of the coefficients A, B, and C in the standard form Ax + By = C?

Back

A and B determine the slope of the line, while C represents the line's position relative to the axes.

Front

How can you convert the equation 3x - 4y = -24 to slope-intercept form?

Back

Rearrange to y = (3/4)x + 6.

Front

What is the slope of the line represented by the equation 3x - 4y = -24?

Back

The slope is 3/4.

Front

What is the relationship between the slope and the intercepts of a line?

Back

The slope indicates the steepness of the line, while the intercepts indicate where the line crosses the axes.

Front

How do you graph a linear equation using intercepts?

Back

Plot the x-intercept and y-intercept on the graph and draw a line through these points.