Question

which equation matches the grap (0,6) (1,4) (2,2) (3,0) y=6x - 2 y= -2x + 1 y= -1/2x +6 y=-2x + 6 <14 of 16 >

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
From the graph, the line crosses the y - axis at \((0,6)\), so \(b = 6\). This eliminates the equations \(y = 6x-2\) (since its \(b=-2\)) and \(y=-2x + 1\) (since its \(b = 1\)).

Step2: Calculate the slope

We can use two points on the line, say \((0,6)\) and \((3,0)\). The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1 = 6,x_2=3,y_2 = 0\) into the slope formula: \(m=\frac{0 - 6}{3-0}=\frac{-6}{3}=-2\).
Now we check the remaining equations:

• For \(y=-\frac{1}{2}x + 6\), the slope \(m =-\frac{1}{2}\), which does not match our calculated slope of \(-2\).
• For \(y=-2x + 6\), the slope \(m=-2\) and the y - intercept \(b = 6\), which matches our findings. We can also verify by plugging in the other points:
• For \((1,4)\): Substitute \(x = 1\) into \(y=-2x + 6\), we get \(y=-2(1)+6=4\), which is correct.
• For \((2,2)\): Substitute \(x = 2\) into \(y=-2x + 6\), we get \(y=-2(2)+6 = 2\), which is correct.
• For \((3,0)\): Substitute \(x = 3\) into \(y=-2x + 6\), we get \(y=-2(3)+6=0\), which is correct.

Answer:

\(y=-2x + 6\)