Question

Is this relation a function? Explain how you know.

Answer 1

Answer:

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

Step-by-step 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

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{3-\left(-3\right)}{-2-3}$

$m=-\frac{6}{5}$

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'.

$y = mx+b$

$-3\:=-\frac{6}{5}\left(3\right)\:+\:b$

$-\frac{18}{5}+b=-3$

$b=\frac{3}{5}$

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