Question

How do you find the slope and y-intercept of $ 4x-6y+3=0 $?

Answer 1

Hint: In this question, we need to find the slope and y-intercept of $ 4x-6y+3=0 $. For this, we will try to convert the given equation in the slope-intercept form by adding/subtracting/multiplying/dividing the terms into both sides of the equation. The slope-intercept form of an equation of a line is given as y = mx+c where m is the slope of the line and c represents the value of y-intercept.

Complete step by step answer:
Here we are given an equation as $ 4x-6y+3=0 $ . We need to find the slope and y-intercept of this equation of a line. For this, let us convert this equation into the slope-intercept form i.e. y = mx+c where m is the slope and c is the y-intercept.
The equation is $ 4x-6y+3=0 $ .
As we do not require 3 on the left side of the equation so subtracting 3 from both sides of the equation we get $ 4x-6y+3-3=0-3 $.
Simplifying the like terms we get $ 4x-6y=-3 $.
We also do not require 4x on the left side of the equation so subtracting 4x from both sides of the equation we get $ 4x-6y-4x=-3-4x $.
Simplifying the like terms we get $ -6y=-3-4x $ .
We require only variable y without any coefficient on the left side of the equation so dividing both sides by -6 we get $ \dfrac{-6y}{-6}=\dfrac{-3-4x}{-6} $ .
Cancelling -6 from the numerator and denominator on left side and separating the terms in the right side we get $ y=\dfrac{-3}{-6}+\left( \dfrac{-4x}{-6} \right) $ .
Cancelling the factor -3 from first term and -2 from second term on the right side we get $ y=\dfrac{1}{2}+\left( \dfrac{2x}{3} \right) $ .
Rearranging the equation we get $ y=\dfrac{2x}{3}+\dfrac{1}{2} $ .
Comparing this equation with y = mx+c we get $ m=\dfrac{2}{3}\text{ and c}=\dfrac{1}{2} $ .
As we know m is the slope of the line and c is the y-intercept so we get,
Slope of the line = $ \dfrac{2}{3} $ .
y intercept of the line = $ \dfrac{1}{2} $ .

Note:
 Students should take care of the signs while simplifying the equation. Take care of what terms need to be added, subtracted, multiplied, and divided. Do not get confused between x-intercept and y-intercept. This equation gives us the y-intercept only.