Q54. - Algebra 2

Question

Find the  x- intercept and the  y- intercept of the graph of equation. Then graph the equation.54 

$\text{y}=3-2\text{x}$

Step-by-Step Solution

Answer

x - intercept is $(1.5,0)$ .

 y - intercept is $(0,3)$ .

 The graph is:

Step 1 - Define x- intercept and y - intercept.

x - intercept is the point on the graph where a line cuts the x - axis.

 Similarly, y - intercept is the point on the graph where a line cuts the  -y axis.

Step 2 - Obtain the x - intercept and y- intercept.

Here, the equation is:

$y=3-2x$     (1)

Now, if a line cuts the x - axis at a point, the coordinate of that point is  $(x,0)$ since y  is always 0 at any point on the x - axis.

 Similarly, if a line cuts the  y- axis at a point, the coordinate of that point is $(0,y)$  since x  is always 0 at any point on the  y- axis.

 Then, to obtain  x- intercept, put$y=0$   in equation1, that is:

$\begin{array}{c}y=3-2x\\ 0=3-2x\\ 2x=3-2x+2x\\ \frac{2x}{2}=\frac{3}{2}\\ x=\frac{3}{2}\\ =1.5\end{array}$

And to obtain y - intercept, put $x=0$  in equation1, that is:

$\begin{array}{c}y=3-2x\\ y=3-2\times 0\\ y=3\end{array}$

Thus, the x - intercept is $(1.5,0)$  and  y- intercept is  $(0,3)$

Step 3 - Plot the graph.

As the x - intercept is $(1.5,0)$  and y - intercept is $(0,3)$ . Then the graph is:

Step 4 - State the conclusion.

Therefore, the x - intercept is $(1.5,0)$  and y - intercept is $(0,3)$ . 

 And the graph is: