Q7. - Algebra 1

Question

Graph each equation by making a table.

$x=8-y$

Step-by-Step Solution

Answer

The solution of the equation by graphing are the intercepts at $x=8$ and $y=8$.

Step 1. State the concept for plotting a straight line using equation.

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.

Step 2. Plot the points.

Graph the equation by using x and y-intercept method. First, find the x and y intercept from the equation and then plot the points on the grid and join then to complete the graph. 

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

$$\begin{gathered} x=8-y \\ x=8-0\text{ [Plug in }y=0] \\ x=8 \end{gathered}$$

x-Intercept: $x=8$.

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

$$\begin{gathered} x=8-y \\ 0=8-y\text{ [Plug in }x=0] \\ -8=8-y-8 \\ -8=y \\ y=-8 \end{gathered}$$

y-Intercept: $y=-8$

Step 3. Plot the graph.

Graph the line $x=8-y$ with x and y intercepts points are (8, 0) and (0, 8).

 

Thus, x and y intercepts are $x=8$ and $y=8$.