Ch 6 Review Questions

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, b) in the equation of a line y = mx + b.

Front

What does a linear relationship between x and y look like on a scatter plot?

Back

A linear relationship appears as a straight line on a scatter plot, indicating that as x increases or decreases, y does so in a consistent manner.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

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

Back

The slope-intercept form is 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, solve for y: y = (-A/B)x + (C/B).

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between x and y. A positive slope means y increases as x increases, while a negative slope means y decreases as x increases.

Front

What does it mean if a scatter plot has no clear linear relationship?

Back

If a scatter plot shows no clear linear relationship, the points are scattered without forming a straight line, indicating that changes in x do not consistently affect y.

Front

How do you determine the y-intercept from a linear equation in slope-intercept form?

Back

In the equation y = mx + b, the y-intercept is the value of b, which is the point where the line crosses the y-axis.

Front

What is the formula for finding the y-intercept when given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1). Rearranging gives you y = mx + (y1 - mx1), where (x1, y1) is the point.

Front

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

Back

The slope of a line is the tangent of the angle (θ) it makes with the positive x-axis, given by m = tan(θ).