Chapter 3.1, Problem 67PFA

To determine

To Find: Which of the following equations has the same y-intercept as the line shown in the graph?

  A $x-y=4$

B $3x-y=6$

C $2x+y=4$

D $x+y=-2$

Answer to Problem 67PFA

The required answer is option A i.e. $x-y=4$ .

Explanation of Solution

Given information:

  

Calculation:

To find the y- intercept, look for the point where the line crosses the y-axis.

In the above graph the line crosses at $\left(0,-4\right)$

Therefore the y- intercept is -4, because it is the y-coordinate of the point where the line crosses the y-axis.

Let us take the equation $x-y=4$

  $\begin{array}{l}x-y=4\\ x-y-x=4-x\end{array}$

(Subtracting x from both sides)

  $-y=4-x$

(Simplify)

  $-y\left(-1\right)=\left(4-x\right)\left(-1\right)$

(Multiply -1 on both sides)

  $y=-\left(4-x\right)$

(Simplify)

So, we can rewrite the equation as $y=-\left(4-x\right)$

To, find y-intercept, let $x=0$

  $y=-\left(4-0\right)$

(Replace x by 0)

  $y=-4$

(Simplify)

Therefore, the correct equation is $x-y=4$