Question

Find the equation of the line passing through the points (3,-2) and (4,6)

Answer 1

The equation is of the form y = mx + b, where m is the slope and b is the y-intercept. Therefore:

- For m:

Given the points (3, -2) and (4, 6)

`m=(y2-y1)/(x2-x1)=(6-(-2))/(4-3)=(6+2)/(1)=(8)/(1)=8`

- For b:

We use the point (4,6)

`\begin{gathered} y=mx+b \\ 6=8(4)+b \\ 6=32+b \\ 6-32=32+b-32 \\ b=-26 \end{gathered}`

Substitute the values, so the equation is:

`y=8x-26`

Answer: y = 8x - 26