Unit 3 · Core unit
Straight-line relationships and the coordinate plane. Slope carries a rate with units, which is what makes linear models interpretable.
What a strong answer looks like
A strong answer gives slope a meaning in context, with units, rather than reporting it as a bare number.
Know
Slope is the change in output per unit change in input, and it is constant for a linear function. In a model it carries the units of the situation.
Apply
Compute from two points, then state what it means per unit in context.
Watch out
Reversing the subtraction in only the numerator or only the denominator, which flips the sign.
Study move
Compute a slope from two points and express it as a sentence with units.
Know
Slope-intercept, point-slope, and standard form describe the same line while exposing different features.
Apply
Choose point-slope when given a point and a slope; convert afterwards if a different form is requested.
Watch out
Reading the intercept from a form that does not display it.
Study move
Write one line in all three forms and confirm they agree at two points.
Know
Parallel lines share a slope; perpendicular slopes are negative reciprocals.
Apply
Take the reciprocal and change the sign, then use a known point to finish.
Watch out
Taking the reciprocal without changing the sign, or vice versa.
Study move
Find the line through a given point perpendicular to a given line.
Modeling drill
A plan charges a fixed fee plus a rate per mile. Write the model, interpret both parameters, and find the cost at a given distance.
