Back to Exercise: Graphing and connecting representations

Exercises: Graphing and Connecting Representations

Where an equation is available, substitute rather than reading the graph. Substitution is exact; a graph is approximate.

Grade 10·18 problems·~34 min·Digital SAT Math·topic·sat-alg-lin2-graph

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Warm-Up: Review What You Know

These review reading a line and its intercepts.

To find where a line crosses the $y$ -axis, which substitution do you make?

Set $y = 0$ , since you are solving for the $y$ -intercept of the line.

Set both $x = 0$ and $y = 0$ , then solve the resulting system of equations.

Set $x = 0$ , since every point on the $y$ -axis has $x$ -coordinate zero.

Set $x = 1$ , since the intercept lies one step across from the origin.

For the line $y = 3x - 5$ , what is the $y$ -coordinate of the point where the line crosses the $y$ -axis?

Fluency Practice

Work these by the fastest reliable route.

Starting from the $y$ -intercept of $y = -3x + 5$ , which move lands you on a second point of the line?

Up 3 and right 1, arriving at the point $(1, 8)$ .

Right 3 and down 1, arriving at the point $(3, 4)$ .

Down 3 and right 1, arriving at $(1, 2)$ .

Down 3 and left 1, arriving at the point $(-1, 2)$ .

$A coordinate grid showing the line y = two-thirds x plus 1, with a step of run 3 and rise 2 landing exactly on the lattice point (3, 3), and a fainter step of run 1 landing between gridlines.$

For the line $y = \frac{2}{3}x + 1$ , you start at the $y$ -intercept and want to land exactly on a gridline intersection. How far right should you step?

For the line $3x + 4y = 12$ , what is the $x$ -coordinate of the $x$ -intercept?

For the line $3x + 4y = 12$ , what is the $y$ -coordinate of the $y$ -intercept?

Does the point $(5, 4)$ lie on the line $3x + 4y = 12$ ?

Yes -- substituting gives 12, so the point satisfies the equation exactly.

Yes -- the point appears to sit on the line when the equation is graphed.

It cannot be determined without first graphing the line on a fine grid.

No -- substituting gives 31, not 12.

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