Question

The equation on the line containing the points (3,4) and (4,8)

Answer 1

first we find the slope with this formula

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

where the point(x2,y2) is the rightmost point between the two points

so, for this case (x2,y2)=(4,8) and (x1,y1)=(3,4)

`\begin{gathered} m=(8-4)/(4-3) \\ m=(4)/(1) \\ m=4 \end{gathered}`

and the general equation of a line is

`y=mx+b`

we can find b replace the points(x,y) with any point of the line, example (3,4)

`\begin{gathered} (4)=(4)(3)+b \\ 4=12+b \\ b=-8 \end{gathered}`

next, make the equation with b and m

`y=4x-8`

you can replace a point to chek

`\begin{gathered} (8)=4(4)-8 \\ 8=16-8 \\ 8=8 \end{gathered}`

so, correct