Graphing using Intercepts

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, meaning the y-coordinate is 0.

Front

How do you find the x-intercept of the equation 3x + 8y = 24?

Back

Set y = 0 and solve for x: 3x + 8(0) = 24, which gives x = 8. So, the x-intercept is (8, 0).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, meaning the x-coordinate is 0.

Front

How do you find the y-intercept of the equation 3x + y = 5?

Back

Set x = 0 and solve for y: 3(0) + y = 5, which gives y = 5. So, the y-intercept is (0, 5).

Front

What are the x- and y-intercepts of the equation 2x - y = 6?

Back

To find the x-intercept, set y = 0: 2x - 0 = 6, giving x = 3. To find the y-intercept, set x = 0: 2(0) - y = 6, giving y = -6. So, the intercepts are (3, 0) and (0, -6).

Front

What is the general form of a linear equation?

Back

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

Front

What does it mean for a line to be in slope-intercept form?

Back

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

Front

How do you graph a line using intercepts?

Back

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

Front

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

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

Back

Intercepts provide key points for graphing the line and help understand the relationship between the variables.