12/5 (8A) Slope, Equations and other stuff

Front

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

Back

The point-slope form is given by the equation: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

Front

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

Back

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

Front

Convert the equation y - 4 = 1(x - 4) to slope-intercept form.

Back

The slope-intercept form is y = mx + b. For this equation, it converts to y = 1x.

Front

What is the slope of a line that rises 4 units for every 1 unit it runs?

Back

The slope is 4, which can be expressed as m = 4.

Front

What does a trend line represent in a scatter plot?

Back

A trend line represents the general direction or pattern of the data points in a scatter plot.

Front

What is the slope of a line that falls 1 unit for every 4 units it runs?

Back

The slope is -1/4, which can be expressed as m = -1/4.

Front

What does it mean if a scatter plot shows no correlation?

Back

No correlation means there is no apparent relationship between the two variables being plotted.

Front

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

Back

Use the point-slope form: y - y₁ = m(x - x₁), substituting the slope and the coordinates of the point.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0, representing where the line crosses the y-axis.

Front

What is the relationship between the slope and the steepness of a line?

Back

A larger absolute value of the slope indicates a steeper line, while a slope of 0 indicates a horizontal line.