Question

A line passes through the points (8,5) and (4,4). What is its equation im slope-intercept from?

Answer 1

Given the points ( 8 , 5 ) and ( 4 , 4 )

The general slop-intercept form of the equation of the line is:

y = mx + c

where m is the slope and c is y-intercept

The slope will be calculated as following:

`\text{slope}=m=(y2-y1)/(x2-x1)=(5-4)/(8-4)=(1)/(4)`

So, the equation of the line will be:

`y=(1)/(4)x+c`

Using the one of the given points to find the value of c

Let , we will use the point ( 4 , 4 )

so, when x = 4 , y = 4

`\begin{gathered} 4=(1)/(4)\cdot4+c \\ 4=1+c \\ c=4-1=3 \end{gathered}`

So, the slope - intercept equation of the line is:

`y=(1)/(4)x+3`