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
[tex]y = mx+b[/tex]
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
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(3,\:-3\right),\:\left(x_2,\:y_2\right)=\left(-2,\:3\right)[/tex]
[tex]m=\frac{3-\left(-3\right)}{-2-3}[/tex]
[tex]m=-\frac{6}{5}[/tex]
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'.
[tex]y = mx+b[/tex]
[tex]-3\:=-\frac{6}{5}\left(3\right)\:+\:b[/tex]
[tex]-\frac{18}{5}+b=-3[/tex]
[tex]b=\frac{3}{5}[/tex]
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
