Answer:
(a) see below
(b) see attached
(c) (15, 180) is not on the line
(d) a = -40
Step-by-step explanation:
Given equation:
[tex]y = 10x+20[/tex]
Part (a)
To complete the table of values, simply substitute each value of x into the given equation:
[tex]x=-3 \implies y=10(-3)+20=-10[/tex]
[tex]x=-1 \implies y=10(-1)+20=10[/tex]
[tex]x=0 \implies y=10(0)+20=20[/tex]
[tex]x=1 \implies y=10(1)+20=30[/tex]
[tex]x=3 \implies y=10(3)+20=50[/tex]
[tex]\large \begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} x & -3 & -2 & -1 & 0 & 1 & 2 & 3\\\cline{1-8} y & -10 & 0 & 10 & 20 & 30 & 40 & 50\\ \cline{1-8} \end{array}[/tex]
Part (b)
Plot 2 points from the table and draw a straight line through them.
Part (c)
To determine if (15, 180) is on the line, substitute x = 15 into the given equation of the line:
[tex]\begin{aligned} x=15 \implies y & =10(15)+20\\& = 150 + 20\\& = 170\end{aligned}[/tex]
Therefore (15, 180) is not on the line
Part (d)
If (-6, a) is on the line, substitute x = -6 and y = a into the equation and solve for a:
[tex]\begin{aligned} y & = 10x+20\\\implies a & = 10(-6)+20\\a & = -60 + 20\\a & = -40\end{aligned}[/tex]
Therefore, a = -40
