Point-slope form review

Review point-slope form and how to use it to solve problems.

What is point-slope form?

Point-slope is a specific form of linear equations in two variables:

y - b = m (x - a)

When an equation is written in this form,

m

gives the slope of the line and

(a, b)

is a point the line passes through.

This form is derived from the slope formula.

Want to learn more about point-slope form? Check out this video.

Finding point-slope equation from features or graph

Example 1: Equation from slope and point

Suppose we want to find the equation of the line that passes through

(1, 5)

and whose slope is

- 2

. Well, we simply plug

m = - 2

a = 1

, and

b = 5

into point-slope form!

y - 5 = - 2 (x - 1)

Example 2: Equation from two points

Suppose we want to find the line that passes through the points

(1, 4)

and

(6, 19)

. First, we use the two points to find the slope:

\begin{aligned} Slope & = \frac{19 - 4}{6 - 1} \\ = \frac{15}{5} \\ = 3 \end{aligned}

Now we use one of the points, let's take

(1, 4)

, and write the equation in point-slope:

y - 4 = 3 (x - 1)

Problem 1

Write the point-slope equation of the line that passes through $(7, 3)$ ‍ whose slope is $2$ ‍.

Want to try more problems like this? Check out this exercise.

Finding features and graph from point-slope equation

When we have a linear equation in point-slope form, we can quickly find the slope of the corresponding line and a point it passes through. This also allows us to graph it.

Consider the equation

y - 1 = 2 (x - 3)

. We can tell that the corresponding line passes through

(3, 1)

and has a slope of

2

. Now we can graph the line:

Problem 1

What is the slope of the line $y - 5 = - 4 (x - 8)$ ‍?

The line passes through which point?

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