Given the equation of a line:
[tex]y=-\frac{2}{5}x+6[/tex]To graph the line, use the slop intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Thus, the slope is:
[tex]-\frac{2}{5}[/tex]While the y-intercept is:
(0, 6)
Let's find the x-intercept.
Substitute y for 0 and solve for x to find the x-intercept.
We have:
[tex]\begin{gathered} 0=-\frac{2}{5}x+6 \\ \\ \text{Multiply through by 5:} \\ 0(5)=-\frac{2}{5}x\ast5+6(5) \\ \\ 0=-2x+30 \\ \\ \text{Subtract 30 from both sides:} \\ 0-30=-2x+30-30 \\ \\ -30=-2x \\ \\ \text{divide both sides by -2:} \\ \frac{-30}{-2}=\frac{-2x}{-2} \\ \\ 15=x \end{gathered}[/tex]Therefore, the x-intercept is; (15, 0)
Find the value of y when x is 5 and 10:
Substitute x for 5 and solve for y
[tex]\begin{gathered} y=-\frac{2}{5}\ast5+6 \\ \\ y=-2+6 \\ \\ y=4 \\ \\ (5,4) \end{gathered}[/tex][tex]\begin{gathered} y=-\frac{2}{5}\ast10+6 \\ \\ y=-4+6 \\ \\ y=2 \\ \\ (10,2) \end{gathered}[/tex]thus, we have the points:
(0, 6)
(5, 4)
(10, 2)
Mark the points on the graph and draw a straight line.
We have the graph below:
