This activity reinforces the understanding that students began to develop in an earlier lesson about the connections between the structure of two-variable linear equations, their graphs, and the situations they represent.

Students first practice relating the parameters of an equation in slope-intercept form to the features of the graph and interpreting them in terms of the situation (MP2). Next, they practice making a case for how they know that a graph represents an equation given in standard form.

Some students may argue that substituting the (x, y) pair of any point on the line gives a true statement, suggesting that the graph does match the equation. Or they may reason about the points on the graph in terms of almonds and figs and come to the same conclusion. For example, (8, 3) and (11, 1) are points on the line. If Clare buys 8 pounds of almonds and 3 pounds of figs, or 11 pounds of almonds and 1 pound of figs, the price is $75.

Ask these students how they would check whether the points with fractional x- and y-values (which are harder to identify precisely from the graph) would also produce true statements when those values are substituted. Use this difficulty to motivate rearranging the equation into slope-intercept form.

The work in this activity requires students to reason quantitatively and abstractly about the equation and the graph (MP2) and to construct a logical argument (MP3).