Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 10 right parenthesis and left parenthesis 1 comma 7 right parenthesis.
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.
(1 point)
The ordered pair is ().
To find an additional ordered pair that satisfies the equation, we can use any point on the line. Let's use the point (0,10):
3x + y = 10
3(0) + 10 = y
y = 10
So the additional ordered pair is (0, 10).
To find the ordered pair where the x-coordinate is 3, we can plug in x = 3:
3x + y = 10
3(3) + y = 10
9 + y = 10
y = 1
So the ordered pair is (3, 1).
To find an additional ordered pair that satisfies the equation 3x + y = 10 using the graph provided, we can see that the line passes through the points (0,10) and (1,7).
First, let's find the slope of the line by using the two known points:
Slope(m) = (y2 - y1) / (x2 - x1)
m = (7 - 10) / (1 - 0)
m = -3 / 1
m = -3
Now, we can use the slope-intercept form of a linear equation, y = mx + b, where "m" is the slope and "b" is the y-intercept. We can substitute the slope (-3) and one of the known points (1,7) into the equation to solve for "b".
7 = -3(1) + b
7 = -3 + b
b = 7 + 3
b = 10
Now that we have the y-intercept (10), we can write the equation of the line as y = -3x + 10.
To find the ordered pair with an x-coordinate of 3, we substitute x = 3 into the equation and solve for y:
y = -3(3) + 10
y = -9 + 10
y = 1
Therefore, the additional ordered pair (x, y) that satisfies the equation 3x + y = 10 is (3,1).
To find the additional ordered pair (x, y) that satisfies the equation 3x+y=10 using the graph, we can follow these steps:
1. Plot the given points on the coordinate plane: (0, 10) and (1, 7).
2. Draw the downward slanting line that passes through these points. This line represents the equation 3x+y=10.
3. Locate the x-coordinate value of 3 on the x-axis.
4. From this point, draw a vertical line until it intersects the line representing the equation.
5. Where the vertical line intersects the slanting line, read the corresponding y-coordinate value.
6. Using the graph, visually estimate the y-coordinate value and identify the corresponding ordered pair.
From the given graph, it looks like the vertical line from x=3 intersects the line 3x+y=10 at approximately (3, 1).
Therefore, the additional ordered pair (x, y) that satisfies the equation is (3, 1).