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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
Remaining Attempts : 3

1 answer

To determine whether Annie's graph of \(3x + y = 10\) is correct, we need to analyze the equation and the graph described.

First, let's rewrite the equation in slope-intercept form \(y = mx + b\):

\[ y = -3x + 10 \]

From the equation, we can see that the slope \(m\) is \(-3\) and the y-intercept \(b\) is \(10\).

The given graph has a line that passes through the points \((0, 10)\) and \((1, 7)\).

To find the slope of the line between these two points:

  1. Calculate the change in \(y\): \[ 7 - 10 = -3 \]
  2. Calculate the change in \(x\): \[ 1 - 0 = 1 \]
  3. The slope is: \[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{-3}{1} = -3 \]

The slope of Annie’s graph is also \(-3\), and the y-intercept is \(10\).

Since both the slope and y-intercept of Annie's graph are correct, we conclude:

Option 3: Yes; Annie's graph is correct.

So the answer is:

3