Writing the equation of a line

Going backward from a line to its equation takes two pieces of information: a slope and a point. If you're given two points, you can get the slope from them.

Work through it

Slope 3, through $(2, 5)$ .

Start with the form and fill in $m$ . $y = 3 x + b$

Substitute the point. $5 = 3 (2) + b$

Solve for $b$ . $b = - 1$

Write the line. $y = 3 x - 1$

Through $(1, 2)$ and $(3, 8)$ .

Slope first. $m = \frac{8 - 2}{3 - 1} = 3$

Use either point. $2 = 3 (1) + b$

Solve. $b = - 1$ , so $y = 3 x - 1$

A plan costs $40 for 5 GB and $70 for 15 GB. Write the cost $C$ for $g$ GB.

Slope is dollars per GB. $\frac{70 - 40}{15 - 5} = 3$

Use a point. $40 = 3 (5) + b$

Solve. $C = 3 g + 25$

The 25 means something: the base fee.

Watch out for this

Using $m$ for $b$ : from slope 3 through $(2, 5)$ , writing $y = 3 x + 5$ .

5 is $y$ at $x = 2$ , not at $x = 0$ . Substitute and solve for $b$ .

The short version
Find the slope, then substitute one point into

y = m x + b

and solve for

b

Your turn

PreviousGraphing lines NextSystems of equations

Want help with this?

Book a free consultation, and we'll help you make a plan.

Book a free consultation