Question

Write an equation for the line that passes through (3,-14) and (2,5). Give the answer in standard form

Answer 1

The equation of a line in standard form looks like this...

`aX+bY=c`

Points

(x1,y1) = (3 , -14)

(x2,y2) = (2 , 5)

`\text{if y=mx+b; then m is the slope m=(y2-y1)/(x2-x1)}`
`m=(5-(-14))/(2-3)=-(19)/(1)=-19`
`y=-19x+b`

if we substitute for the first point:

`\begin{gathered} -14=-19\cdot(3)+b \\ -14=-57+b \\ b=57-14=43 \end{gathered}`

Therefore,

`y=-19\cdot x+43`

Now, we want to write this equation in standard form:

`\begin{gathered} y=-19x+43 \\ +19x+y=+19x-19x+43 \\ 19x+y=43 \end{gathered}`

Therefore a=19 ; b=1 and c=43