Question

Write an equation of the line that passes through points (4,1) and (-2,7)

Answer 1

Answer:

y = -x+5

Step-by-step explanation:

We have 2 points so we can find the slope

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

    = (7-1)/(-2-4)

     = 6/-6

     =-1

We can use point slope form for the equation of a line

y-y1=m(x-x1)

y-1 = -1(x-4)

Distribute

y-1 = -1 x +4

Add 1 to each side

y-1+1 = -x +4+1

y = -x+5

Answer 2

Answer:

y = - x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

To calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (4, 1) and (x₂, y₂ ) = (- 2, 7)

m = $\frac{7-1}{-2=4}$ = $\frac{6}{-6}$ = - 1, hence

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

using (4, 1), then

1 = - 4 + c ⇒ c = 1 + 4 = 5

y = - x + 5 ← equation of line