Point Slope Form to Standard Form

It is a common task to convert equation of line from point slope form to standard form.

Video Tutorial on Point Slope to Standard Form

Example of Converting from Point Slope to Standard Form

Convert $$ y - 3 = 5(x - 4)$$ to standard form.

Distribute $$\red m$$, which represents the slope to $$ \blue$$.

Step 1 answer

$$ y-y_1 = \red m \blue < ( x - x_1)>\\ y-3 = \red 5 \blue <( x - 4) >\\ y-3 = \red 5 \cdot \blue x -\red 5 \cdot \blue 4 \\ y-3 = 5x -20 \\ $$

Move y₁ to the other side by adding its opposite to both sides of the equation and simplify.

Step 2 answer

"Move" the x term to the other side by adding its opposite to both sides.

Step 3 answer

Use our Calculator

You can use the calculator below to find the equation of a line from any two points. Just type numbers into the boxes below and the calculator (which has its own page here) will automatically calculate the equation of line in point slope and standard forms.

Toggle Points

(This link will show the same work that you can see on this page)

Practice Converting Equations

Practice 1

Convert (y - 2) = -5(x - 1) to standard form.

Distribute $$\red m$$, which represents the slope to $$ \blue$$.

Step 1 answer $$ y-y_1 = \red m \blue < ( x - x_1)>\\ y-2 = \red <-5>\cdot \blue x - \red < -5>\cdot \blue 1 \\ y-2 = -5x + 5 $$

Move y₁ to the other side by adding its opposite to both sides of the equation and simplify.

Step 2 answer

"Move" the x term to the other side by adding its opposite to both sides.