Slope, Eqns, Plotting Points, F(X)

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

How do you find the equation of a line given a point and a slope?

Back

To find the equation of a line given a point (x₀, y₀) and a slope m, use the point-slope form: y - y₀ = m(x - x₀).

Front

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

Back

The point-slope form of a linear equation is y - y₀ = m(x - x₀), where (x₀, y₀) is a point on the line and m is the slope.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you calculate the slope between two points (x₁, y₁) and (x₂, y₂)?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form (y = mx + b).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Given f(x) = -x + 12, what is f(-2)?

Back

f(-2) = -(-2) + 12 = 2 + 12 = 14.

Tags

CCSS.HSF.IF.A.2

Front

What are coordinates in a Cartesian plane?

Back

Coordinates are a pair of numbers (x, y) that define a point's position on a Cartesian plane, where x is the horizontal position and y is the vertical position.

Tags

CCSS.5.G.A.1

Front

How do you plot a point (x, y) on a graph?

Back

To plot a point (x, y), start at the origin (0, 0), move x units horizontally (right for positive, left for negative), and then move y units vertically (up for positive, down for negative).

Tags

CCSS.5.G.A.2

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed in physics or cost per item in economics, indicating how one variable changes in relation to another.

Tags

CCSS.8.EE.B.5