Q56. - Algebra 2

Question

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

$5\text{x}-2\text{y}=10$

Step-by-Step Solution

Answer

x - intercept is $(8,0)$ .

 y - intercept is$(0,-16)$  .

 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:

$5x-2y=10$      (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:

$\begin{array}{c}5x-2y=10\\ 5x-(2\times 0)=10\\ 5x=10\\ \frac{5x}{5}=\frac{10}{5}\\ x=2\end{array}$

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

$\begin{array}{c}5x-2y=10\\ (5\times 0)-2y=10\\ -2y=10\\ -\frac{2y}{2}=\frac{10}{2}\\ -y=5\\ y=-5\end{array}$

Thus, the x - intercept is $(2,0)$  and  y- intercept is $(0,-5)$ .

Step 3 - Plot the graph.

As the x - intercept is $(2,0)$  and y - intercept is  $(0,-5)$. Then the graph is:

Step 4 - State the conclusion.

Therefore, the  x- intercept is $(2,0)$  and  y- intercept is $(0,-5)$ .

 And the graph is: