Exercise 37 Page 260

To write an equation of the line containing the points in the table, we have to find its slope

m

and

y -

b,

and then substitute it into the slope-intercept form.

y = m x + b

To find the slope, we should substitute two of the points in the Slope Formula.

m = \frac{f ( x ) _{2} - f ( x ) _{1}}{x _{2} - x _{1}}

Substitute $(5, 10)$ & $(12, 31)$

m = \frac{3 1 - 1 0}{1 2 - 5}

Subtract terms

m = \frac{2 1}{7}

Calculate quotient

m = 3

The slope is

3,

which means we have half of what we need to write the equation.

y = 3 x + b

Finally, to find the

y -

intercept we substitute one of the points into the equation and solve for

b .

y = 3 x + b

$x = 3$ , $y = 4$

4 = 3 (3) + b

▼

Solve for

b

4 = 9 + b

$LHS - 9 = RHS - 9$

- 5 = b

Rearrange equation

b = - 5

Now we can complete the equation.

y = 3 x - 5