Use the graph of 3x+y=10 to determine an additional ordered pair (x, y) that satisfies the equation. Find the ordered pair (x, y) if the x-coordinate is 3. Write as an order pair.
if x=3, then
9+y = 10
so y=1
so (3,1) is the desired pair
To find an additional ordered pair (x, y) that satisfies the equation 3x+y=10 using the graph, we can follow these steps:
1. Plot the given equation on a coordinate plane. The equation 3x+y=10 can be rewritten in slope-intercept form as y = -3x + 10.
Start by finding two points that satisfy the equation by substituting different values of x. Let's choose x = 0 and x = 2:
When x = 0, y = -3(0) + 10 = 10. So we have the point (0, 10).
When x = 2, y = -3(2) + 10 = 4. So we have the point (2, 4).
Plot these two points on the coordinate plane and draw a straight line passing through them.
2. To find an additional ordered pair, we can look for another point on the line. Pick any x-value and substitute it into the equation to solve for y.
Let's choose x = 3. Plug x = 3 into the equation y = -3x + 10:
y = -3(3) + 10
y = -9 + 10
y = 1
Therefore, when x = 3, y = 1. The additional ordered pair is (3, 1).
So, the ordered pair (x, y) when the x-coordinate is 3 is (3, 1).
To find an additional ordered pair that satisfies the equation 3x+y=10, we can use the graph.
Step 1: Represent the given equation on a graph.
The equation can be rearranged to solve for y:
y = 10 - 3x
The graph of this equation will be a straight line.
Step 2: Plot the graph.
We will use the x and y intercepts of the equation to plot the graph.
x-intercept: When y = 0, we can substitute y = 0 into the equation:
0 = 10 - 3x
3x = 10
x = 10/3 ≈ 3.33
Therefore, the x-intercept is approximately (3.33, 0).
y-intercept: When x = 0, we can substitute x = 0 into the equation:
y = 10 - 3(0)
y = 10
Therefore, the y-intercept is (0, 10).
Step 3: Find an additional ordered pair.
One way to find an additional ordered pair is by selecting any point on the graph. Let's choose the point where the x-coordinate is 3. By reading off the corresponding y-coordinate from the graph, we can find the additional ordered pair.
From the graph, we can see that when x = 3, the corresponding y-coordinate is approximately 1.
Therefore, the additional ordered pair is (3, 1).