Question

How do you write $2x - 5y = 15$in slope-intercept form?

Answer 1

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 solution:
Take the given equation: $2x - 5y = 15$
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.
$\Rightarrow - 5y = 15 - 2x$
Multiply the above equation with $( - 1)$. When you multiply with minus sign, sign of the terms changes. Positive terms become negative and the negative term becomes positive.
$\Rightarrow 5y = - 15 + 2x$
Term multiplicative on one side, if moved to the opposite side then it goes to the denominator.
$\Rightarrow y = \dfrac{{ - 15 + 2x}}{5}$
Simplify the above equation by giving denominator to each term of the numerator.
$\Rightarrow y = \dfrac{{ - 15}}{5} + \dfrac{{2x}}{5}$
Common factors from the numerator and the denominator cancel each other.
$y = - 3 + \dfrac{{2x}}{5}$
The above equation can be re-written as: $y = \dfrac{{2x}}{5} - 3$
The above equation is now in the form of the slope-intercept form.

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 multiply a negative number with any terms, the sign of the term changes. Positive terms become negative and vice-versa.