Question

(-5, 7) (3, -1) in slope intercept form

Answer 1

Answer: The equation of the line in slope-intercept form is y = -x + 2.

Step-by-step explanation: Hello! To find the equation of a line in slope-intercept form, we need two pieces of information: the slope (m) and the y-intercept (b).

Given two points (-5, 7) and (3, -1), we can find the slope using the formula:

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

Let's assign the coordinates as follows:

x1 = -5, y1 = 7

x2 = 3, y2 = -1

Substituting the values into the slope formula, we get:

m = (-1 - 7) / (3 - (-5))

m = -8 / 8

m = -1

Now that we have the slope, we can use one of the given points (-5, 7) to find the y-intercept (b). Let's use the point-slope form:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 7 = -1(x - (-5))

y - 7 = -1(x + 5)

y - 7 = -x - 5

To get the equation in slope-intercept form (y = mx + b), we need to isolate y:

y = -x - 5 + 7

y = -x + 2

Therefore, the equation of the line in slope-intercept form is y = -x + 2.

Answer 2

y = - x + 2

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (- 5, 7 ) and (x₂, y₂ ) = (3, - 1 )

m =
`(-1-7)/(3-(-5))` =
`(-8)/(3+5)` =
`(-8)/(8)` = - 1 , then

y = - x + c ← is the partial equation

to find c ,substitute either of the 2 points into the partial equation

using (3, - 1 ) for x and y in the partial equation

- 1 = - 3 + c ( add 3 to both sides )

2 = c

y = - x + 2 ← equation of line