Question

How do you find the slope and y intercept of $ 3x+4y=5 $ ?

Answer 1

Hint:
 The slope is calculated by finding the ratio of the vertical change to the horizontal change between any two distinct points on a line. The slope of a line is the steepness of the line and intercept is where the line intersects the y or x-axis. First of all, we should know the definition of slope for a line equation $ ax+by+c=0 $ . The slope of line equation $ ax+by+c=0 $ is equal to $ -\dfrac{b}{a} $ .

Complete step by step answer:
Now considering the given question we have the equation given as $ 3x+4y=5 $ .
To find the slope of a standard equation, we need to derive the value of $ y $ .
From the question, it had been given that $ 3x+4y=5 $
First of all, subtract $ 3x $ from both sides of the equation.
 $ \Rightarrow 3x+4y=5 $
 $ \Rightarrow 3x+4y-3x=5-3x $
 $ \Rightarrow 4y=5-3x $
Now we will divide both sides of the equation by $ 4 $
 $ \Rightarrow \dfrac{4y}{4}=\dfrac{5-3x}{4} $
 $ \Rightarrow \text{y=}\dfrac{5}{4}-\dfrac{3x}{4} $
We know that slope is the value which is multiplying the $ x $ , so the slope is $ -\dfrac{3}{4} $ .
So, it is clear that the slope of the given equation is $ -\dfrac{3}{4} $

Now, to find the $ y $ intercept, we set $ x $ to be zero and find the value of y.
 $ \Rightarrow y=\dfrac{5}{4}-\dfrac{3x}{4} $
 $ \Rightarrow y=\dfrac{5}{4}-\dfrac{3\left( 0 \right)}{4} $
Simplify more further to get the intercept,
 $ \Rightarrow y=\dfrac{5}{4}-0 $
 $ \Rightarrow y=\dfrac{5}{4} $
So, the y intercept is at $ \left( 0,\dfrac{5}{4} \right) $

Note:
      During answering questions of this type we should be sure with the calculations and concept. The slope of the line characterizes the direction of a line. The slope of a line is given as $ y $ intercept by $ x $ intercept. The $ y $ intercept of $ ax+by+c=0 $ is given by substituting the zero in the place of $ x $ then we will obtain the value of $ y $ similarly $ x $ intercept can be obtained by putting $ y=0 $ in the expression. And the slope can be given as $ -\dfrac{\text{y-intercept}}{\text{x-intercept}} $ here in this question it is $ \dfrac{-\left( \dfrac{5}{4} \right)}{\left( \dfrac{5}{3} \right)}=\dfrac{-3}{4} $ because the $ x $ intercept is given as $ 3x+4\left( 0 \right)=5\Rightarrow x=\dfrac{5}{3} $ that is $ \left( \dfrac{5}{3},0 \right) $ .