Question

Write the equation of a line through points (5,5) and 1,0) in point slope form.

Answer 1

The correct answer is first option

y = 5/4(x - 1)

Explanation:

It is given two coordinates (5, 5) and (1, 0)

To find the slope

Slope = (y₂ - y₁)/(x₂- x₁)

slope = (5 - 0)/(5 - 1) = 5/4

To find the equation

(y - y₁)/(x - x₁) = 5/4

(y - 0)/(x - 1) = 5/4

y = 5/4(x - 1)

The correct answer is first option

Answer 2

Hello!

The answer is:

The correct option is the first option,

`y=(5)/(4) (x-1)`

Why?

To solve this problem, we need to remember that the point-slope form of a line is given by the following equation:

`y-y_(1)=m(x-x_(1))\\\\y-0=(5)/(4)(x-1)`

We are given two points of the line,

`(5,5)\\(1,0)`

Where,

`x=5\\x_(1)=1\\y=5\\y_(1)=0\\`

Then, substituting the given points into the equation ,to calculate m (slope), we have:

`m=(y-y_(1))/(x-x_(1))`

`m=(5-0)/(5-1)=(5)/(4)`

The slope of the function is
`(5)/(4)`

Now, substituting "x1" and "y1" and the slope in the point-slope equation, we have:

`(y-0)=(5)/(4) (x-1)`

`y=(5)/(4) (x-1)`

Hence, the correct option is the first option,

`y=(5)/(4) (x-1)`

Have a nice day!