Given:
Rate of change = [tex]\frac{3}{2}[/tex]
Graph passes through the point (4, 10.5)
To find:
The equation of the function of the graph.
Solution:
Rate of change is same as the slope
Slope (m) = [tex]\frac{3}{2}[/tex]
Here [tex]x_1=4, y_1=10.5[/tex]
Using point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]$y-10.5=\frac{3}{2} (x-4)[/tex]
[tex]$y-10.5=\frac{3}{2} x-\frac{3}{2} (4)[/tex]
[tex]$y-10.5=\frac{3}{2} x-6[/tex]
Add 10.5 on both sides.
[tex]$y=\frac{3}{2} x+4.5[/tex]
The equation of the function is [tex]y=\frac{3}{2} x+4.5[/tex].
