Chapter 3.1, Problem 4ACYP

To determine

Graph the equation by using x and y − intercept.

Answer to Problem 4ACYP

x and y intercepts are x= − 3 and y = 1.5

Explanation of Solution

Given:

The equation: $-x+2y=3$

Concept Used:

The  x -intercepts are where the graph crosses the  x -axis, and the  y -intercepts are where the graph crosses the  y -axis.

Then, algebraically,

• an  x -intercept is a point on the graph where  y  is zero, and
• a  y -intercept is a point on the graph where  x  is zero.

More specifically,

• an  x -intercept is a point in the equation where the  y -value is zero, and
• a  y -intercept is a point in the equation where the  x -value is zero.

Calculation:

The equation: $-x+2y=3$

Find the x − intercept, plug in y = 0 in the equation.

  $\begin{array}{l}-x+2y=3\\ -x+2·0=3[\text{plug}\text{in}y=0]\\ -x=3\\ -1·-x=-1·3\text{[}\text{Multiply}\text{both}\text{sides}\text{by}\text{]}\\ x=-3\end{array}$ X − Intercept: x= − 3

Find the y − intercept, plug in x = 0 in the equation

  $\begin{array}{l}-x+2y=3\\ -0+2y=3[\text{plug}\text{in}x=0]\\ 2y=3\\ \frac{2y}{2}=\frac{3}{2}[\text{Divide}\text{each}\text{side}\text{by}6]\\ y=1.5\end{array}$ y − Intercept: y = 1.5

Graph the line $-x+2y=3$ with x and y intercepts points are (− 3, 0) and ( 0 , 1.5 )

  

Thus, x and y intercepts are x = − 3 and y = 1.5

.