Question

Is this relation a function? Explain how you know.

Answer 1

The relation is a linear function with the equation: y = -6/5x + 3/5

Explanation:

Question 5)

The given graph is a straight line.

We know that the graph of a linear function is a straight line that can be written in the form

`y = mx+b`

where m is the slope and b is the y-intercept

The slope of the line can be determined by taking two points

(3, -3)

(-2, 3)

Finding the slope

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(3,\:-3\right),\:\left(x_2,\:y_2\right)=\left(-2,\:3\right)`

`m=(3-\left(-3\right))/(-2-3)`

`m=-(6)/(5)`

From the graph, the y-intercept can be obtained by setting x=0 and check the corresponding y-value of y.

or substituting m = -6/5 and (3, -3) in the slope-intercept form to determine y-intercept 'b'.

`y = mx+b`

`-3\:=-(6)/(5)\left(3\right)\:+\:b`

`-(18)/(5)+b=-3`

`b=(3)/(5)`

now substituting m = -6/5 and b = 3/5 in the slope-intercept form to determine the equation of the linear function

y=mx+b

y = -6/5x + 3/5

Therefore, the relation is a linear function with the equation: y = -6/5x + 3/5