Question

Please help❤️ Write an equation for the line through the points (9,5) and (6, 7) in point-slope form

y = y0 + m(x - x0).
y =_ + _

Answer 1

`y=5-(2)/(3)(x-9)`

Explanation:

We are given that the line passes through the two points (9, 5) and (6, 7).

And we want to find the equation of the line in point-slope form:

`y=y_0=m(x-x_0)`

First, let's find the slope. The slope is given by the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Let's let (9, 5) be (x₁, y₁) and let (6, 7) be (x₂, y₂). Substitute these values into the slope formula:

`m=(7-5)/(6-9)`

Subtract:

`m=2/-3`

Simplify:

`m=-2/3`

So, our slope is -2/3.

Note, we can use the point-slope form. Notice that we also need an (x₀, y₀).

We can use either of our two known points. So, let's let (9, 5) be (x₀, y₀).

Substitute 9 for x₀, 5 for y₀, and -2/3 for m yields:

`y=5-(2)/(3)(x-9)`

And we're done!

Answer 2

y = 5 -2/3 ( x-9)

Explanation:

point slope form

y = y0 + m(x - x0).

m is the slope

m = (y2-y1)/(x2-x1)

( 7-5)/(6-9)

2/-3

=-2/3

The slope is -2/3

Using the point (9,5)

y = 5 -2/3 ( x-9)