Question

How do you write $ 5x - 3y + 6 = 0 $ into slope intercept form?

Answer 1

Hint: In any linear equation, m is the slope and b is the y-intercept and this equation is known as the slope-intercept equation. Here will find the y intercept value for the given equation and by converting it in the form of the standard equation, $ y = mx + b $ .

Complete step-by-step answer:
Take the given equation: $ 5x - 3y + 6 = 0 $
Convert the above equation in the form of the $ y = mx + b $
Therefore, make the given equation in the form of “y” on the left hand side of the equation. Take all the terms on the right hand side of the equation. When you move any term from one side to another, the sign of the term also changes. Positive term changes to the negative term and vice-versa.
 $ - 3y = - 6 - 5x $
Take negative sign common from both the sides of the equation, the above equation can be re-written as:
 $ y = \dfrac{6}{3} + \dfrac{5}{3}x $
Now, the term common in the numerator and the denominator cancels each other.
 $ y = 2 + \dfrac{5}{3}x $
The above equation is now in the form of the slope-intercept form.
So, the correct answer is “ $ y = 2 + \dfrac{5}{3}x $ ”.

Note: Always remember the standard form of the linear equation, slope and intercept equation as the y intercept depends on the standard equation. Also be careful about the sign convention of the linear equation. When you move any term from one side to another, the sign of the term also changes. Positive terms become negative and the negative terms become positive.
Always remember that the product of slope of two perpendicular lines is always minus one whereas the slope of two parallel lines is equal and same. Parallel lines can be defined as the two lines which are in the same plane and are at equal distance from each other and they never intersect each other whereas the lines which intersect each other at ninety degree are known as the perpendicular lines.