Question

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

Answer 1

Answer:

$y=5-\frac{2}{3}(x-9)$

Step-by-step 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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{7-5}{6-9}$

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:

$y=5-\frac{2}{3}(x-9)$

And we're done!

Answer 2

Answer:

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

Step-by-step 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)