Answer:
B. [tex]y=\dfrac{9}{2}x+5[/tex]
Step-by-step explanation:
The equation of the line in the slope-intercept form is
[tex]y=mx+b.[/tex]
First, find the slope of the line:
[tex]m=\dfrac{23-14}{4-2}=\dfrac{9}{2}[/tex]
Now, find the y-intecept b:
[tex]y=\dfrac{9}{2}x+b\\ \\14=\dfrac{9}{2}\cdot 2+b\\ \\14=9+b\\ \\b=14-9\\ \\b=5[/tex]
Hence, the equaiton is
[tex]y=\dfrac{9}{2}x+5[/tex]
Check all points:
[tex](2,14):\ \ \dfrac{9}{2}\cdot 2+5=9+5=14\\ \\(4,23):\ \ \dfrac{9}{2}\cdot 4+5=18+5=23\\ \\(6,32):\ \ \dfrac{9}{2}\cdot 6+5=27+5=32\\ \\(8,41):\ \ \dfrac{9}{2}\cdot 8+5=36+5=41[/tex]
