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.
Annie has created a graph of 3x+y=10
on the coordinate plane. Did Annie create her graph correctly?
Option 1: No; Annie's y
-intercept is correct but her slope is incorrect.
Option 2: No; Annie's slope is correct but her y
-intercept is incorrect.
Option 3: Yes; Annie's graph is correct.
Enter "1" for Option 1, "2" for Option 2, or "3" for Option 3.
(1 point)
Option
2: No; Annie's slope is correct but her y-intercept is incorrect.
wrong
Apologies for the confusion. Based on the description, the downward slanting line passes through the points (0,10) and (1,7). To determine if Annie's graph is correct, we can compare it to the given equation 3x+y=10.
First, let's determine the slope of the line passing through the given points (0,10) and (1,7). The slope, m, can be calculated as:
m = (y2 - y1)/(x2 - x1) = (7 - 10)/(1 - 0) = -3/1 = -3
Now, we need to compare this slope to the equation 3x+y=10. The equation is in the form y = mx + b, where m represents the slope. According to the equation, the slope is 3.
Since the slope calculated from the points is -3 and the slope in the equation is 3, Annie's graph is incorrect. Therefore, the answer is:
Option 1: No; Annie's y-intercept is correct, but her slope is incorrect.
To determine if Annie's graph of the equation 3x+y=10 is correct, we need to compare it with the given information in the image.
The image shows a line passing through the points (0,10) and (1,7).
To find the slope of the line, we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (0,10) and (1,7), we can substitute the values into the formula:
slope = (7 - 10) / (1 - 0)
slope = -3
So, the slope of the line passing through the points (0,10) and (1,7) is -3.
The equation given is 3x+y=10, which is in the standard form of a linear equation (y=mx + b), where m represents the slope and b represents the y-intercept.
Comparing the slopes, we see that the slope in the equation (3) is different from the slope of the line in the image (-3).
Therefore, Annie did not create her graph correctly. Her slope is incorrect.
Option 1: No; Annie's y-intercept is correct but her slope is incorrect.
To determine if Annie created her graph correctly, we need to compare her line with the given points on the coordinate plane.
The equation of Annie's line is 3x + y = 10.
To check if the line passes through the points (0, 10) and (1, 7), we substitute the x and y coordinates into the equation and verify if they satisfy it.
For the point (0, 10):
3(0) + 10 = 10
0 + 10 = 10
10 = 10
This point satisfies the equation.
For the point (1, 7):
3(1) + 7 = 10
3 + 7 = 10
10 = 10
This point also satisfies the equation.
Since both points satisfy the equation, we can conclude that Annie's line is correct.
Therefore, the correct answer is Option 3: Yes; Annie's graph is correct.