The matched equation and coordinate pairs:
a) y=2x+5 = (3,11),
b) [tex]y=\frac{2}{3}x+4[/tex] = (-6,0),
c) y=-3x+7 = (4,-5) and
d) [tex]y=\frac{1}{5}x-2[/tex] = (5,-1).
Step-by-step explanation:
We are given with coordinate pairs and its equation. Check that applying the x value in the coordinate pair gives the answer y.
Let us match the coordinate points by applying into each equations.
a) y=2x+5.
Substitute (5,-1)
-1=2(5)+5.
-1≠15.
Substitute(4, -5)
-5=2(4)+5.
-5≠13.
Substitute(3,11)
11=2(3)+5.
11=11.
∴(3,11) is the coordinate pair for y=2x+5.
b) [tex]y=\frac{2}{3} x+4[/tex].
Substitute (5,-1)
[tex]-1=\frac{2}{3}(5)+4[/tex].
[tex]-1=\frac{10}{3} +4.[/tex]
The denominator should be same in order to continue further. 4 has no denominator it means the denominator is 1. it can be represented as [tex]\frac{4}{1}[/tex].
Multiply 3 on both numerator and denominator in [tex]\frac{4}{1}[/tex].
[tex]-1=\frac{10}{3} +\frac{4}{3}[/tex].
[tex]-1=\frac{10+12}{3}[/tex].
-1×3=22.
-3≠22.
Substitute (4,-5)
[tex]-5=\frac{2}{3}(4)+4.[/tex]
[tex]-5=\frac{20}{3}[/tex].
-15≠20.
Substitute(-6,0)
[tex]0=\frac{2}{3} (-6)+4.[/tex]
0=-12+12.
0=0.
∴(-6,0) is the coordinate pair for [tex]y=\frac{2}{3}x+4.[/tex]
c) y=-3x+7.
substitute(5,-1)
-1=(-3)5+7.
-1= -15+7.
-1≠ -8.
Substitute(4, -5)
-5= (-3)(4)+7.
-5= -12+7.
-5= -5.
∴(4,-5) is the coordinate pair for y=-3x+7.
⇒(5,-1) is the coordinate pair for [tex]y=\frac{1}{5}x-2[/tex].
