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Illustrative Math
Grade 8
Let’s find solutions to more linear equations.
Illustrative Math Unit 8.3, Lesson 13 (printable worksheets)
Let’s think about the linear equation 2x - 4y = 12. If we know (0,-3) is a solution to the equation, then we also know (0, -3) is a point on the graph of the equation. Since this point is on the y-axis, we also know that it is the vertical intercept of the graph. But what about the coordinate of the horizontal intercept, when y = 0? Well, we can use the equation to figure it out.
2x - y = 12
2x - 4(0) = 12
2x = 12
x = 6
Since x = 6 when y = 0, we know the point (6, 0) is on the graph of the line. No matter the form a linear equation comes in, we can always find solutions to the equation by starting with one value and then solving for the other value.
For each equation choose a value for x and then solve to find the corresponding y value that makes that equation true.
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. Explain your reasoning.
One partner has 6 cards labeled A through F and one partner has 6 cards labeled a through f. In each pair of cards (for example, Cards A and a), there is an equation on one card and a coordinate pair, (x, y), that makes the equation true on the other card.
Consider the equation ax + by = c, where a, b and c are positive numbers.
The x-intercept is -c/a.
The y-intercept is -c/b
The slope is -a/b
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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