Question

plot the point on this function with an x - value of 7.
what is the y - value of this point?

Explanation:

Step1: Determine the function's equation

The line passes through the origin \((0,0)\) and \((2, -1)\) (we can see from the graph that when \(x = 2\), \(y=- 1\)). The slope \(m\) of the line is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,-1)\), we get \(m=\frac{-1 - 0}{2 - 0}=-\frac{1}{2}\). So the equation of the line (function) is \(y = mx + b\), and since \(b = 0\) (passes through origin), the equation is \(y=-\frac{1}{2}x\).

Step2: Find y - value when x = 7

Substitute \(x = 7\) into the equation \(y=-\frac{1}{2}x\). So \(y=-\frac{1}{2}\times7=-\frac{7}{2}=- 3.5\).

Answer:

\(-3.5\)