Writing Linear Equations and Scatter Plots: math test, Grade 9 – download the PDF

1 Slope and a point / 3 pts

Write each line in slope-intercept form.

(a) Slope \(-4\), through \((2, 3)\).

(b) Slope \(2\), through \((-1, -5)\).

2 Two points / 3 pts

A line passes through \((-1, 7)\) and \((3, -1)\).

(a) Find its equation.

(b) Find its x-intercept.

3 Modeling plant growth / 4 pts

The height \(y\) (in cm) of a bean plant was measured \(x\) days after planting: \((1, 3)\), \((2, 5)\), \((3, 8)\), \((4, 9)\), \((5, 12)\), \((6, 14)\). A model is \(y = 2.2x + 1\).

(a) Describe the correlation.

(b) Find the residual at \(x = 3\).

(c) Interpret the slope.

(d) Predict the height on day 10 and comment on its reliability.

4 Correlation and prediction / 3 pts

Over a summer, a pool measured \(r = 0.88\) between the number of ice cream cones sold and the number of swimmers who needed help. The data cover temperatures from 60 °F to 95 °F.

(a) Do the cones cause the swimmers’ problems?

(b) Name a lurking variable.

(c) Is predicting for 80 °F interpolation or extrapolation? And for 40 °F?

5 Delivery fee / 4 pts

A store charges \(D(x) = 5\) dollars for deliveries up to 3 miles, and \(D(x) = 5 + 1.5(x - 3)\) for \(x > 3\) miles.

(a) Find \(D(2)\).

(b) Find \(D(7)\).

(c) Simplify the rule for \(x > 3\).

(d) What distance costs $14?

6 An absolute value function / 3 pts

Consider \(y = |x + 2| - 4\). Find the vertex, the y-intercept, and the x-intercepts.