Completing Ordered Pairs and Graphing Linear Equations
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 \( y = -\frac{2}{5}x+1 \).
