Question

Find the equation of the line passing through the points (-5,1) and (2.1) Write the equation in point-slope form

Answer 1

Hello !

Answer:

`\Large \boxed{\sf y=1}`

Explanation:

The slope-intercept form of a line is of the form
`\sf y=mx+b` where m is the slope and b is the y-intercept.

We're looking for the two coefficients m and b.

The lines passes through two points :

• (-5,1)
• (2,1)

Let's replace x and y with their values in the equation :

`\begin{cases}\sf 1=-5m+b \\\sf 1=2m+b\end{cases}`

We get a system of two linear equations to solve.

Let's subtract the second line from the first one and solve for m :

`\sf 1-1=-5m+b-(2m+b)\\\iff 0=-5m+b-2m-b\\\iff 0=-7m\\\iff \boxed{\sf m=0}`

Let's substitute 0 for m in the second equation :

`\sf 1=2* 0+b\\\iff \boxed{\sf b=1}`

The slope-intercept form of the line is :

`\sf y=0x+1`

`\boxed{\sf y=1}`

Have a nice day ;)