Topic 5 Review

Front

What is the formula for calculating the slope of a line between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the steepness of the line and the direction of the relationship between the variables.

Front

How do you find the y-intercept of a line given its equation in slope-intercept form (y = mx + b)?

Back

The y-intercept is the value of y when x = 0, which is represented by the constant b in the equation.

Front

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

Back

The slope is m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line is decreasing; for every 1 unit increase in x, y decreases by 3 units.

Front

What is the equation of a line with a slope of 2 that passes through the point (1, 4)?

Back

Using the point-slope form, the equation is y - 4 = 2(x - 1), which simplifies to y = 2x + 2.

Front

What does the y-intercept represent in a real-world context?

Back

The y-intercept represents the initial value of the dependent variable when the independent variable is zero.

Front

How do you determine if a slope is positive, negative, or zero?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope is a horizontal line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y as x changes.