More Solutions to Linear Equations

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Determine if a Point is a Solution to an Equation.

Here are graphs representing three linear relationships. These relationships could also be represented with equations.

For each statement below, decide if it is true or false.

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Determine if a Point is a Solution to an Equation.

The points  (6, 13), (21, 33) and (99, 137) all lie on the same line. The equation of the line is

Explain or show your reasoning using the applet below.

Find the  -intercept of the graph of the equation. Explain or show your reasoning.

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Investigate the Solutions of a System of Two Linear Equations.

Using the applet below, move the points A,B,C,D around and notice where the two lines intersect.

(1). What do you notice about the numbers of points of intersection?

(2). What do we know about solutions to systems of linear equations?

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Consider the equation a + b = c , where a, b and c are positive numbers.

(1). Find the coordinates of the – and -intercepts of the graph of the equation.

(2). Find the slope of the graph of this equation.

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Find the coordinates of B, C, and D given that AB = 5 and BC = 10.

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Match each graph of a linear relationship to a situation that most reasonably reflects its context. Drag the situation to the graph that it matches.