Question

Equation of the line that passes through (4,8) and (2,-10)

Answer 1

Hello !

Answer:

`\boxed{\sf y=9x-28}`

Explanation:

We are looking for the equation of the line that passes through the two following points :

• (4,8)
• (2,-10)

We know that the slope-intercept form of a line is of the form
`\sf y=mx+b`.

We need to find the coefficients m and b.

Let's replace x and y with 4 and 8, and then with 2 and -10.

`\sf \begin{cases}\sf8=4m+b \\\sf -10=2m+b\end{cases}`

We obtain a system of two equations to solve.

Let's subtract the second line from the first one :

`\sf 8-(-10)=4m+b-(2m+b)\\\iff 18=4m+b-2m-b\\\iff 18=2m\\\iff \boxed{\sf m= (18)/(2)=9 }`

Let's substitute 9 for m in the second equation :

`\sf -10=2* 9+b\\\iff b+18=-10\\\iff b=-10-18\\\iff \boxed{\sf b=-28}`

The equation of the line is :
`\boxed{\sf y=9x-28}`

Have a nice day ;)