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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
Remaini

1 answer

To determine whether Annie's graph of the equation \(3x + y = 10\) is correct, we first need to derive the slope and the y-intercept from that equation.

  1. Rearrange the equation into slope-intercept form (y = mx + b): \[ y = -3x + 10 \] Here, the slope (m) is -3 and the y-intercept (b) is 10.

  2. Check points on the graph:

    • The y-intercept is at the point (0, 10), which is correct according to the illustration.
    • To check the slope, if x = 1, then: \[ y = -3(1) + 10 = 7 \] So the point (1, 7) is also on the line.

Since both the y-intercept and the slope agree with the points given in the illustration, Annie's graph is indeed correct.

Therefore, the correct option is: 3 (Yes; Annie's graph is correct.)