Question - Completing Ordered Pairs and Graphing Linear Equations
mathcompleting ordered pairsgraphing linear equationslinear equation solution setordered pairs graphing
Solution:
The image shows a linear equation $$ y = -\frac{2}{5}x+1 $$ and we are asked to complete the given ordered pairs (0, _), (5, _), and (10, _). Also, we're supposed to use two of the ordered pairs to graph the solution set for the equation.To find the missing y-values for each x-value, we'll substitute the x-values into the equation.1. When x = 0:$$ y = -\frac{2}{5}(0) + 1 $$$$ y = 0 + 1 $$$$ y = 1 $$So the ordered pair is (0, 1).2. When x = 5:$$ y = -\frac{2}{5}(5) + 1 $$Because $$ \frac{2}{5} \times 5 = 2 $$, we have:$$ y = -2 + 1 $$$$ y = -1 $$So the ordered pair is (5, -1).3. When x = 10:$$ y = -\frac{2}{5}(10) + 1 $$Because $$ \frac{2}{5} \times 10 = 4 $$, we have:$$ y = -4 + 1 $$$$ y = -3 $$So the ordered pair is (10, -3).To graph these points, you would plot (0, 1), (5, -1), (10, -3) on a coordinate plane and draw a straight line through these points, which would represent the solution set for the equation $$ y = -\frac{2}{5}x+1 $$.
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