ACT math slope and lines

What is slope?

Slope measures the steepness of a line. Calculated as $\displaystyle \frac{rise}{run}$.

What does a positive slope indicate?

A positive slope means the line rises as it moves from left to right.

What does a negative slope indicate?

A negative slope means the line falls as it moves from left to right.

Fill in the blank: The slope formula is _____.

The slope formula is $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$.

True or false: A slope of 0 indicates a horizontal line.

True, because horizontal lines have no vertical change.

Difference between slope-intercept form and point-slope form?

Slope-intercept: $\displaystyle y = mx + b$; Point-slope: $\displaystyle y - y_1 = m(x - x_1)$.

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

Slope $\displaystyle m = \frac{7-3}{4-2} = 2$.

What does 'y-intercept' mean?

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

Calculate the slope between points (1, 2) and (3, 4).

Slope $\displaystyle m = \frac{4-2}{3-1} = 1$.

True or false: The equation $\displaystyle y = 3x + 2$ has a slope of 3.

True, because the slope is the coefficient of x.

Fill in the blank: A vertical line has an undefined _____.

A vertical line has an undefined slope.

What is the slope of a line parallel to $\displaystyle y = -5x + 1$?

The slope is -5, because parallel lines share the same slope.

When is the slope considered 'undefined'?

The slope is undefined for vertical lines where $\displaystyle x$ remains constant.

Find the equation of the line with slope 2 through (1, 1).

Using point-slope: $\displaystyle y - 1 = 2(x - 1)$.

What would be the slope of a line if it decreases?

The slope will be negative.

Identify the slope from the equation $\displaystyle y = \frac{1}{2}x - 3$.

The slope is $\displaystyle \frac{1}{2}$.

Describe the slope of a line perpendicular to $\displaystyle y = 4x + 1$.

Perpendicular slope is the negative reciprocal: $\displaystyle -\frac{1}{4}$.

Find the slope of the line connecting (0, 0) and (2, 4).

Slope $\displaystyle m = \frac{4-0}{2-0} = 2$.

If two lines have the same slope, what can be said about them?

They are parallel lines.

What is the y-intercept of the line $\displaystyle y = 2x + 5$?

The y-intercept is 5, where the line crosses the y-axis.