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Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=-2 x+7 ;(1,5),(-2,3)$$
$y=-2 x+7$
Algebra
Chapter 3
Graphs and Functions
Section 1
Graphing Equations
Functions
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Oregon State University
McMaster University
University of Michigan - Ann Arbor
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for this problem. We want to find out if the coordinates 15 and the coordinates Negative 23 could be solutions to the equation. Why equals negative two X plus seven? In order to find out, we're going to find the X and Y coordinates of each set off corners that were given and plugged them in place of the X and Y in our equation. So for the first set, we have 15 or x coordinate is one R Y. Coordinate is five. So we're gonna rewrite our equation. And in place of the Wild X, we're gonna put one in five. So when they rewrite, I'm gonna have five equals. Negative, too. Times one plus seven, we're gonna simplify. Negative. Two times. One is negative. Two plus seven. We'll keep bringing my five. Dale. Negative. Two plus seven is five and five does equal five. So this means that 15 is a solution to the equation. Now, let's try the coordinates. Negative. 23 Our X coordinate is negative to our Why? Coordinate is three. So we're gonna read, write our equation and we're rewriting as three equals Negative, too. Times negative too. Plus seven So we're going to simplify will bring my three down. They get two times negative. Two is positive. Four plus seven and four plus seven is 11. So three does not equal 11 which means that negative 23 is not a solution to the equation.
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