Question

question 1 of x
select the correct answer.
which graph represents the inequality? inequality not fully visible, likely linear inequality
four graphs of linear functions/inequalities shown

Explanation:

Step1: Analyze the equation

The equation is \( y = -x + 10 \). This is a linear equation in slope - intercept form \( y=mx + b \), where the slope \( m=- 1\) and the y - intercept \( b = 10\).

Step2: Check the y - intercept

The y - intercept is the point where \( x = 0\). Substituting \( x = 0\) into the equation \( y=-x + 10\), we get \( y=10\). So the line should pass through the point \((0,10)\).

Step3: Check the slope

The slope \( m=-1\) means that for every 1 unit we move to the right along the x - axis (increase in \( x\) by 1), we move down 1 unit along the y - axis (decrease in \( y\) by 1).
Now let's analyze the graphs:

• The first graph: Let's check the y - intercept. If we assume the third graph (the one with the line starting at \((0,10)\)): When \( x = 0\), \( y = 10\) (matches the y - intercept). Then, when \( x = 10\), \( y=-10 + 10=0\), so the line passes through \((10,0)\). The slope between \((0,10)\) and \((10,0)\) is \(m=\frac{0 - 10}{10-0}=\frac{- 10}{10}=-1\), which matches the slope of the equation \( y=-x + 10\).
• The other graphs: The first graph (top - most) has a y - intercept at \( y = 0\) (when \( x = 0\), \( y = 0\)) which does not match \( y = 10\). The second graph has a y - intercept at \( y=-10\) (when \( x = 0\), \( y=-10\)) which does not match. The fourth graph has a y - intercept that is not 10 (it seems to cross the y - axis above 0 but not at 10).

Answer:

The third graph (the one with the line starting at \((0,10)\) and ending at \((10,0)\))