Question

Work out the equation of the line that goes through (3, 2) and (-1, 10)

Answer 1

Answer:

$The\,\,equation\,\,will\,\,be\,\,2x+y=8$

Step-by-step explanation:

Let, A=(3,2)

      B=(-1,10)

So, The equation will be

$\frac{x-x_{1} }{x_{1} -x_{2} } =\frac{y-y_{1} }{y_{1} -y_{2} } \\=>\frac{x-3 }{3-(-1) } =\frac{y-2 }{2-10} \\=>\frac{x-3 }{4} =\frac{y-2 }{-8}\\=>-8x+24=4y-8\\=>8x+4y=32\\=>2x+y=8$

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Answer 2

Answer:

y = - 2x + 8

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 )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 1, 10 )

m = $\frac{10-2}{-1-3}$ = $\frac{8}{-4}$ = - 2 , then

y = - 2x + c ← is the partial equation

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

Using (3, 2 )

2 = - 6 + c ⇒ c = 2 + 6 = 8

y = - 2x + 8 ← equation of line