Question

Write an equation in point-slope form of the line that passes through the given point and has the given slope. (5,-4); m = -1

Answer 1

`y+4=-(x-5)`

Explanation:

Point-slope form equation is written as:

`y-y_1=m(x-x_1)`

where m is the slope and
`(x_1,y_1)` is the point which the line passes through so to to find the equation of line which passes through the point

(5 , -4) it means the point should satisfy the equation which furthermore means that the point lies on the lie so we can replace y1 with -4 and x1 with 5 and since we have m = -1 we can thus find b and rewrite the equation like this:

`y-y_1=m(x-x1)\\y-(-4)=-1(x-5)\\y+4=-x+5`

since we need it point-slope form we leave it like this

`y+4=-(x-5)`

Answer 2

y + 4 = - (x - 5)

Explanation:

The equation of a line in slope- intercept form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (5, - 4) , then

y - (- 4) = - 1 (x - 5) , that is

y + 4 = - (x - 5)