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
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Annie's graph is correct. Option 3.
To determine whether Annie created her graph correctly, we need to compare it with the given equation, which is 3x + y = 10.
Comparing this equation with the standard slope-intercept form y = mx + b, we can see that the slope (m) is the coefficient of x, which is 3, and the y-intercept (b) is 10.
Based on the given information about Annie's graph passing through the points (0, 10) and (1, 7), we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values:
m = (7 - 10) / (1 - 0)
m = -3
Comparing the calculated slope (-3) with the slope of the given equation (3), we can see that they are different. The slope Annie used for her graph is incorrect.
Therefore, the correct answer is:
Option 1: No; Annie's y-intercept is correct, but her slope is incorrect.