It is a common task to convert equation of line from point slope form 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 answerYou 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)
Convert (y - 2) = -5(x - 1) to standard form.
Distribute $$\red m$$, which represents the slope to $$ \blue$$.
Step 1 answer $$ y-y_1 = \red m \blue < ( x - x_1)>\\ y-2 = \red <-5>\cdot \blue x - \red < -5>\cdot \blue 1 \\ y-2 = -5x + 5 $$-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.