Question

How do you find the slope and y-intercept of the graph of $2x - 5y = 20$ ?

Answer 1

Hint: To solve this question, we must first understand some basic concepts about slope. Then we need to use the basic formula of slope to find the value of slope and then find the y-intercept which is the distance of the intersection of the line with the Y-axis and then only we can conclude the correct answer.

Complete Step by Step answer:
Before we move forward with the solution of this given question, let us first understand some basic concepts:
As we know that, the slope (also known as gradient) of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m.
And the slope is calculated by dividing the vertical change with the horizontal change between two distinct points on a line.
The formula is given by:
$ \Rightarrow Slope = \,\,m = \,\dfrac{{\Delta y}}{{\Delta x}}\,\, = \,\,\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
And we also have a simple formula to find the slope which is given by:
$ \Rightarrow m = \,\dfrac{{ - \left( {coefficient\,\,of\,\,x} \right)}}{{\left( {coefficient\,\,of\,\,y} \right)}}$
Step 1: The given equation is: $2x - 5y = 20$.
Here coefficient of $x = 2$, coefficient of $y = - 5$.
Step 2: $Slope = m = \,\dfrac{{ - \left( {coefficient\,\,of\,\,x} \right)}}{{\left( {coefficient\,\,of\,\,y} \right)}}\,\, = \,\,\dfrac{{ - 2}}{{ - 5}} = \dfrac{2}{5} = 0.4$
And we have our required answer.

Note:
- A line is increasing if it goes up from left to right. The slope is positive, i.e. m > 0.
- A line is decreasing if it goes down from left to right. The slope is negative, i.e. m<0.
- If a line is horizontal the slope is zero. This is a constant function.
- If a line is vertical the slope is undefined.