Question

] Find the equation of the line. 3+ 2-+ 1+ -9 8 7 6 5 4 3 2 ++r 1 2 3 4 5 6 7 8 9 2.- 3+ 1 6 7 91 y = X + |

Answer 1

Step 1: Write out the equation of a line given two points

`\begin{gathered} A(x_(1,)y_1) \\ B(x_2,y_2) \\ \text{equation of the line is} \\ (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Step 2: Pick two points from the graph provided

`\begin{gathered} A(0,-2) \\ B(2.5,0) \end{gathered}`

Step 3: Substitute the coordinates value in the formula

`\begin{gathered} x_1=0;y_1=-2 \\ x_2=2.5;y_2=0 \end{gathered}`
`\begin{gathered} (y--2)/(x-0)=(0--2)/(2.5-0) \\ (y+2)/(x)=(2)/(2.5) \\ \text{crossmultiply} \\ 2.5(y+2)=2x \\ y+2=(2x)/(2.5) \\ y=(20x)/(25)-2 \\ y=(4)/(5)x-2 \end{gathered}`

Hence, the equation of the line is y=(4/5)x+(-2)