Students read slope and y-intercept from equations, graph lines on coordinate grids, and write equations from tables, graphs and a taxi fare rule.
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Materials: ruler
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Students graph lines from slope-intercept form and write equations from tables and graphs. The worked example plots y = 2x − 3 from its y-intercept, counting right 1 and up 2. One line is written y = 8 − (2/3)x, so students reorder it before reading the slope, and one table starts at x = 1, so they work back a step to find the y-intercept. A taxi fare problem asks them to go from distance to cost and back, and to explain what the slope means for the rider.
Line 6, y = 8 − (2/3)x, is the one students read backward, giving the slope as 8 and the y-intercept as −2/3. Have them rewrite it as y = −(2/3)x + 8 first, as the key does.
For line 8, y = (3/4)x − 2, students often count up 4 and right 3. Say the slope as rise over run, up 3 and right 4, and check that the line passes through (4, 1).
Table 11 has no x = 0 column, so some students give −6 as the y-intercept. Ask them to step back from x = 1 to x = 0 by adding 4, which gives −2.
Ways to adjust the 13 numbered items and the taxi problem.
Each one is checked against the official documents. Where the resource covers only part of a standard, the note says so.
Students find the slope and y-intercept from tables and graphs and write the equation, write the taxi fare as y = 2.25x + 3.50, and explain what the slope means for a taxi ride.
Students name the slope and y-intercept in six equations and graph lines from y = mx + b by plotting the y-intercept and using the slope. Giving examples of functions that are not linear is not covered.
Students use rise over run between points to graph lines and read slopes. The similar-triangle explanation and deriving the equations are not covered.
Students write line equations from tables, graphs and a taxi fare rule.
Students find the slope and y-intercept from three tables and two graphs and explain what the taxi's slope means; slope from similar triangles is not covered.
Students graph lines such as y = -2x + 4 from their equations and link tables, graphs and equations; one line (y = 5x) is proportional, which falls outside this expectation.
No. Every line is in slope-intercept form, y = mx + b, apart from line 6, which only needs reordering.
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