Question

Write the equation in slope-intercept for for the line tot goes through (-8-2) and (-4,6)

Answer 1

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

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

Step 2: write out the coordinates given in the question

`\begin{gathered} A(-8,-2) \\ B(-4,6)_{} \\ x_1=-8;y_1=-2 \\ x_2=-4;y_2=6 \end{gathered}`

Step 3: Substitute the given parameters in the formula

`\begin{gathered} (y--2)/(x--8)=(6--2)/(-4--8) \\ (y+4)/(x+8)=(6+2)/(-4+8) \\ (y+4)/(x+8)=(8)/(4) \\ (y+4)/(x+8)=2 \end{gathered}`
`\begin{gathered} \text{crossmultiply} \\ y+4=2(x+8) \\ y+4=2x+16 \\ y=2x+16-4 \\ y=2x+12 \end{gathered}`

Hence, the equation of the line is y=2x+12