Question

How do you graph using slope and intercept of 5x + 2y = -1?

Answer 1

Hint: In this question, we will use the general form of equation of slope and intercept to solve the problem. You should know that the general form of this equation is y = mx + c where m is the slope and c is the constant here that tells you to shift up or down the graph by b units. This is basically slope-intercept form which is used in this question.

Complete step by step answer:
Now let’s solve the question.
As we know about the slope-intercept form that it is a general form of a straight line and is expressed as y = mx + c where ‘m’ is a slope and c is a constant. The intercepts are m and c.
For plotting the straight line, first we need to convert the given equation in a slope-intercept form. Let’s see how!
Write the equation from the question.
$\Rightarrow $5x + 2y = -1
Now, keeping ‘y’ alone takes all the terms on the other side one by one. First take 5x to the other side we get:
$\Rightarrow $2y = -5x – 1
Next step is to take 2 to the other side and divide the equation by 2. We get:
$\Rightarrow y=\dfrac{-5}{2}x-\dfrac{1}{2}.......(i)$
Therefore, we have got our equation in the slope-intercept form i.e. y = mx + c.
Here, m = $\dfrac{-5}{2}$ and c = $\dfrac{-1}{2}$ .
Now, we have to find the intercepts for x and y.
Let’s find y-intercept first. Substitute x = 0 in equation(i) we get:
$\Rightarrow y=\dfrac{-5}{2}(0)-\dfrac{1}{2}$
The term multiplied by 0 will become 0. Now we get the value of ‘y’ as:
$\Rightarrow y=\dfrac{-1}{2}$
$\therefore $ y-intercept form is: $\left( 0,\dfrac{-1}{2} \right)$
Let’s find the x-intercept now. Substitute y = 0 in equation(i) we get:
$\Rightarrow 0=\dfrac{-5}{2}x-\dfrac{1}{2}$
Next step is to take $\dfrac{1}{2}$ common and move it to the other side of the equation. We get:
$\Rightarrow 0\times \dfrac{2}{1}=-5x-1$
The whole left part again becomes 0.
$\Rightarrow 0=-5x-1$
Now, move -5x to the other side of the equation. We will get:
$\Rightarrow 5x=-1$
Now the value of x will be:
$\Rightarrow x=\dfrac{-1}{5}$
$\therefore $ x-intercept will be: $\left( \dfrac{-1}{5},0 \right)$

Now, let’s plot the graph of the equation given in the question with the help of the intercepts.

This is the graph of y-intercept: $\left( 0,\dfrac{-1}{2} \right)$
This is the graph of x-intercept: $\left( \dfrac{-1}{5},0 \right)$

Note: In this question particularly, we have to use slope-intercept form as it is asked to graph the equation by using slope and intercept. Otherwise questions can be solved by substitution also. Plotting of the graph should be done neatly.