Question

What is the slope-intercept form of the function described by this table? X 1 2 3 4 y 8 13 18 23 Enter your answer by filling in the boxes. y=x X +​

Answer 1

Answer:

The slope-intercept form of the function is:

$y=5x+3$

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

• (1, 8)

• (2, 13)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(2,\:13\right)$

$m=\frac{13-8}{2-1}$

$m=5$

We know that the slope-intercept form of the line equation is

$y=mx+b$

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'.

$y=mx+b$

8 = 5(1) + b

b = 8-5

$b = 3$

Now, substituting the values m=5 and b=3 in the slope-intercept form to

$y=mx+b$

$y=5x+3$

Thus, the slope-intercept form of the function is:

$y=5x+3$