Question

write an equation in slope-intercept fotm for the line that passes through the given points(2,3),(1,5) (5,-2),(-16,4)

Answer 1

First line: (2,3) and (1,5).

We have to find the slope

`m=(y_2-y_1)/(x_2-x_1)`

Where,

`\begin{gathered} x_1=2 \\ x_2=1 \\ y_1=3 \\ y_2=5 \end{gathered}`
`m=(5-3)/(1-2)=(2)/(-1)=-2`

Then, we use the point-slope formula to find the equation of the first line

`\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-2(x-2) \\ y=-2x+4+3 \\ y=-2x+7 \end{gathered}`

The first equation is y = -2x + 7.

Second line: (5, -2) and (-16, 4).

We repeat the process we used above to find the second line.

`m=(y_2-y_1)/(x_2-x_1)`

Where,

`\begin{gathered} x_1=5 \\ x_2=-16 \\ y_1=-2 \\ y_2=4 \end{gathered}`
`m=(4-(-2))/(-16-5)=(4+2)/(-21)=-(6)/(21)=-(2)/(7)`

Then,

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-(2)/(7)(x-5) \\ y+2=-(2)/(7)x+(10)/(7) \\ y=-(2)/(7)x+(10)/(7)-2 \\ y=-(2)/(7)x+(10-14)/(7) \\ y=-(2)/(7)x+(-4)/(7) \\ y=-(2)/(7)x-(4)/(7) \end{gathered}`

The second equation is y = -2/7x - 4/7.