Question

Which of the following equations represents a linear function? Please show the steps of the answer! Thank you

Answer 1

Second option:

`y = (1)/(2)x -5`

Explanation:

A linear function should have y as a function of x (or x as a function of y) and the degree of the function (the highest power has to be 1)

Both x and y must be present to make it a linear function

General slope intercept form is y = mx + b where m = slope, b = y-intercept

With these restrictions the second option is the correct one

`y = (1)/(2)x -5`

This line is in slope intercept form y = mx + b where m = slope(in this case 1/2) and y-intercept b(in this cae -5)

Option 1: x = 3 is a straight vertical line parallel to the y-axis. Such a line has a slope of ∞

Option 3 is a function with degree 2 and is a quadratic function

Option 4 : 3x - 6 = 4==> 3x = 6 + 4 = 10 or x = 10/3, again another vertical line with slope = ∞

Answer 2

2nd choice y = 1/2x - 5

Explanation:

y = 1/2x - 5 is the only function listed that if you graph it, it makes a straight line. A linear function forms a straight line when it is plotted on a graph.

The first and last choices are number values of x.

The 3rd choice, if you graph it, makes a parabola.