Answer:
The slope-intercept form of the function is:
[tex]y=5x+3[/tex]
Step-by-step explanation:
Given the table
x y
1 8
2 13
3 18
4 23
Let us take two points (1, 8) and (2, 13) to find the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(2,\:13\right)[/tex]
[tex]m=\frac{13-8}{2-1}[/tex]
[tex]m=5[/tex]
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
substituting the values m=5 and the point (1, 8) to determine the y-intercept i.e. 'b'.
[tex]y=mx+b[/tex]
8 = 5(1) + b
b = 8-5
[tex]b = 3[/tex]
Now, substituting the values m=5 and b=3 in the slope-intercept form to
[tex]y=mx+b[/tex]
[tex]y=5x+3[/tex]
Thus, the slope-intercept form of the function is:
[tex]y=5x+3[/tex]
