Answer:
[tex]y=4.5x+5[/tex]
Step-by-step explanation:
The slope of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through the points (2,14) and (4,23), then its slope is
[tex]\dfrac{23-14}{4-2}=\dfrac{9}{2}=4.5[/tex]
The equation of the line in slope-intercept form is
[tex]y=mx+b,[/tex]
wher m is the slope and b is y-intercept.
Thus, the equation is
[tex]y=4.5x+b[/tex]
This line passes through the point (2,14), its coordinates satisfy the equation, so
[tex]14=4.5\cdot 2+b\\ \\9+b=14\\ \\b=14-9\\ \\b=5[/tex]
Hence, the equation is
[tex]y=4.5x+5[/tex]
