Question

Write the linear equation that gives the rule for this table.

Answer 1

Answer:

The linear equation that gives the rule for this table will be:

• y=x+25

Step-by-step explanation:

Taking two points from the table

• (2, 27)

• (3, 28)

Finding the slope between two points

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

$\left(x_1,\:y_1\right)=\left(2,\:27\right),\:\left(x_2,\:y_2\right)=\left(3,\:28\right)$

$m=\frac{28-27}{3-2}$

$m=1$

We know the slope-intercept form of linear equation is

$y=mx+b$

where m is the slope and b is the y-intercept

substituting the point (2, 27) and m=1 in the slope-intercept form to determine the y-intercept 'b'

$y=mx+b$

27 = 1(2)+b

27-2 = b

b = 25

Now, substituting m=1 and b=25 in the slope-intercept form to determine the linear equation

y=mx+b

y=1(x)+25

y=x+25

Thus, the linear equation that gives the rule for this table will be:

• y=x+25