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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To determine if Annie's graph is correct, we can compare it to the given equation. The equation is 3x + y = 10, which is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
From the image, we can see that the line passes through the points (0, 10) and (1, 7).
To find the slope of the line passing through these two points, we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
slope = (7 - 10) / (1 - 0)
slope = -3 / 1
slope = -3
From the equation 3x + y = 10, we can rearrange it to y = -3x + 10.
Comparing the slope and y-intercept of the equation to Annie's graph, we can see that Annie's slope of -3 is correct, but her y-intercept of 10 is incorrect.
Therefore, Annie did not create her graph correctly, and the correct option is Option 2: No; Annie's slope is correct but her y-intercept is incorrect.