Question

determine whether the given point is on the line. explain your reasoning.
(0, -2); ( y = \frac{1}{4}x - 3 )
select choice substituting 0 and -2 for x and y results in an equation that select choice true.

Explanation:

Step1: Identify x and y values

The point is \((8, -2)\), so \(x = 8\) and \(y=-2\). The line equation is \(y=\frac{1}{4}x - 8\).

Step2: Substitute x and y into the equation

Substitute \(x = 8\) and \(y=-2\) into the right - hand side of the equation: \(\frac{1}{4}(8)-8\)
First, calculate \(\frac{1}{4}(8)\): \(\frac{1}{4}\times8 = 2\)
Then, calculate \(2 - 8=-6\)
Now, compare the left - hand side (\(y=-2\)) and the right - hand side (\(-6\)). Since \(-2
eq - 6\), the point \((8,-2)\) does not satisfy the equation of the line.

Answer:

The point \((8, - 2)\) is not on the line \(y=\frac{1}{4}x - 8\) because when we substitute \(x = 8\) and \(y=-2\) into the equation \(y=\frac{1}{4}x - 8\), we get \(-2=\frac{1}{4}(8)-8\), and \(\frac{1}{4}(8)-8=2 - 8=-6\), and \(-2
eq - 6\).