Question

A line passes through the points (5, 1.5) and (1, 2.5).
Create an equation of the line.

Answer 1

Hello !

Answer:

`\boxed{\sf y=-0.25x+2.75}`

Explanation:

A line passes through two points :

• (5, 1.5)
• (1, 2.5)

Moreover, the slope-intercept form of a line is of the form
`y=mx+b`.

We want to find the coefficients m and b.

Let's replace x and y with 5 and 1.5, and then with 1 and 2.5.

`\begin{cases}1.5=5m+b \\2.5=m+b\end{cases}`

We get a system of two equations to solve.

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

`1.5-2.5=5m+b-(m+b)\\\iff -1=4m\\\iff \boxed{m=-(1)/(4)=-0.25}`

Let's substitute
`-0.25` for m in the second equation :

`2.5=-0.25 +b\\\iff \boxed{b=2.75}`

An equation of the line is
`y=-0.25x+2.75`.

Have a nice day ;)