Question

What is the zero of the linear function below?

Answer 1

Answer: $x=-4$

Step-by-step explanation:

Remember that the line intersects the x-axis when $y=0$.Therefore, the zero of a linear function is the value of the variable "x" when the value  of "y" is zero.

 The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

In this case, given the graph of the function,you can identify that the y-intercept is:

$b=1$

 By definition, the slope can be calculated with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Then, in order to find the slope, you can pick the points (4,2) and (-8,-1) and say that:

$y_2=-1\\y_1=2\\\\x_2=-8\\x_1=4$

So, substituting these values into the formula, you get:

$m=\frac{-1-2}{-8-4}=\frac{1}{4}$

Then the linear function has this form:

$y=\frac{1}{4}x+1$

Finally, in order to find the x-intercept, you can substitute $y=0$ into the function and solve for "x". This is:

$0= \frac{1}{4}x +1\\\\(-1)(4)=x\\\\x=-4$