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).

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.

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).

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).

Front

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

Back

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

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.

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).

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.