It is a common task to have to convert the equation of a line from standard form to point slope form.
Convert 3x + 5y = 15 to point slope form.
Isolate the $$\red y$$ term.
Step 1 answer $ 3x + \red < 5 y>= 15 $Multiply all terms by the multiplicative inverse of the coefficient of y.
Step 2 answer $$ 5y = -3x + 15 \\ \red \cdot 5y = \red \cdot -3x + \red \cdot 15 \\ \frac = \frac + \frac $$ Step 3 answer $$ \frac<5y> = \frac + \frac \\ y = - \frac 3 5 x + 3 $$Substitute a convenient value for x into your equation and then solve for y.
You're doing this to get the values of $$ ( \blue, \blue) $$ for the point slope formula : $$ y - \blue y_1 = m(x - \blue x_1) $$
Remember that you can pick any value that you want. You're just choosing a value for $$x$$ and then finding its associated $$y $$ value.
Step 4 answerLet's choose $$x = \blue 5$$ . Yes, you could choose x = 0 and make your life really easy! After you solve for the y value, then .
$$ y = - \frac 3 5 x + 3 \\ \text < Let's choose >x = \blue 5 \\ y = -\frac 3 5 \cdot \blue 5 + 3 \\ y = -3 + 3 \\ y = \blue 0 \\ \text < Or, using >x = \blue 0 \\ y = - \frac 3 5 x + 3 \\ y = -\frac 3 5 \cdot \blue 0 + 3 \\ y = \blue 3 $$
Substitute the x value you picked and y value you solved for into the general form of point slope formula.
Step 3 answerNote that both of the above equations are equivalent. They both are valid. Neither equation is 'better'.