Question

Graph the line with y-intercepts 8And the slope - 1/5

Answer 1

The general equation of the line is,

`y=mx+b`

Given:

`\begin{gathered} m=\text{slope = -}\frac{\text{1}}{5} \\ b=y-\text{intercept = 8} \end{gathered}`

Substitute the values of m and b into the equation, in order to obtain the equation.

`y=-(1)/(5)x+8`

Let us solve for the x-intercept and y-intercept in order to plot the graph of the line.

X-intercept

The x-intercept is the value of the x coordinate of a point where the value of y-coordinate is equal to zero.

`\begin{gathered} y=0 \\ 0=-(1)/(5)x+8 \\ (1)/(5)x=8 \\ \text{Cross}-m\text{ultiply} \\ x=8*5=40 \\ \therefore The\text{ x-intercept is (40,0)} \end{gathered}`

Y-intercept

The point where a line or curve crosses the y-axis of a graph. In other words: find the y-value when x equals 0.

`\begin{gathered} x=0 \\ y=-(1)/(5)(0)+8 \\ y=0+8=8 \\ \therefore The\text{ y-intercept is (0,8)} \end{gathered}`

Hence, the points to plot the graph are (40 , 0) and (0 , 8).

Let us now plot the graph