Question

Write a linear equation that passes through the points (-3,3) and (9,-13)

please help!

Answer 1

Answer:

$y = -\frac{4}{3} x - 1$

Step-by-step explanation:

y = mx + b

m = delta y / delta x

m = (-13 - 3) / [(9 - (-3)]

m = -16/12

m = -4/3

From (-3 | 3) we know that when x = -3, y = 3

Placing into equation to find b

3 = (-4/3)*-3 + b

3 = 12/3 + b  

b = -1

Answer 2

The equation of the line that passes through the given points is 3y + 4x = -3

From the question,

We are to determine the equation of the line that passes through the points (-3,3) and (9,-13)

The equation can be determined by using the formula for calculating the equation of a line with two given points.

The formula for determining the equation of a straight line with two given points (x₁, y₁) and (x₂, y₂) is

$\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

From the question,

x₁ = -3

y₁ = 3

x₂ = 9

y₂ = -13

Putting the parameters into the formula, we get

$\frac{y-3}{x--3}= \frac{-13-3}{9--3}$

This becomes

$\frac{y-3}{x+3} = \frac{-16}{12}$

Then,

$\frac{y-3}{x+3}=\frac{-4}{3}$

This becomes

$3(y-3) = -4(x+3)$

Clearing the brackets, we get

$3y -9 = -4x -12$

$3y+4x= -12 +9$

$3y +4x =-3$

Hence, the equation of the line that passes through the given points is 3y + 4x = -3

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