Lesson Two Assessment (Slope and Equation of a Line)

Front

What is the formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How can you determine if a line is increasing or decreasing based on its slope?

Back

A line is increasing if its slope is positive (m > 0) and decreasing if its slope is negative (m < 0).

Front

What is the slope of a line represented by the equation y = mx + b?

Back

The slope of the line is represented by the coefficient m in the equation y = mx + b.

Front

How do you convert the standard form of a linear equation (Ax + By = C) to slope-intercept form (y = mx + b)?

Back

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

Front

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

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -1/2, what does this indicate about the line's direction?

Back

A slope of -1/2 indicates that the line is decreasing; for every 2 units you move to the right, you move 1 unit down.

Front

What is the y-intercept in the equation y = 2x + 7?

Back

The y-intercept is 7, which is the value of y when x = 0.

Front

How do you find the slope from a linear equation in standard form, such as 3x + 4y = 16?

Back

Rearrange the equation to slope-intercept form (y = mx + b) to find the slope. For 3x + 4y = 16, the slope is -3/4.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.