Question

Give $8x+4y=4$ , how do you identify the slope and y-intercept?
(a) Using the slope intercept form
(b) Simplifying the equation
(c) Guessing the solution
(d) None of these

Answer 1

Here in this problem, we have the equation $8x+4y=4$ and we are to find the slope and y-intercept of the equation. We will solve the problem using the slope intercept form $y=mx+c$, where m is the slope and c is the y intercept of the equation. We will first analyze the equation and try to make the coefficient of y can be 1. Then by comparing with the slope intercept form we will get our desired result.

Complete step by step solution:
According to the question, we are given equation, $8x+4y=4$
Now, to start with, we can start by analyzing both sides of the equation to check if anything can be taken as a common factor.
By analyzing, we see that 4 is common from both sides.
So, start with, $8x+4y=4$
Then, if we subtract 8x from both sides,
$4y=-8x+4$
Now, we will try to get the slope intercept form,
Hence, we will now divide each side by 4,
$\dfrac{4y}{4}=\dfrac{-8x+4}{4}$
In the left hand side 4 can be cancelled out, so we now get,
$y=\dfrac{-8x}{4}+\dfrac{4}{4}$
Then in the right hand side by simplifying,
$y=-2x+1$
Hence, comparing it with the slope intercept form, $y=mx+c$,
We can conclude that the slope of the equation is -2 and the y intercept would be 1.

So, the correct answer is “Option a”.

Note: In this problem, we are trying to find the solution using the slope intercept form. The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.