Question

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (1, 5) and (-2, 3)

Answer 1

Use the slope formula to find the slope.
(5-3)/(1+2)=2/3
Now put it in the formula point slope equation.
y-5=2/3(x-1)
Simplify
y=(2/3)x-(13/3)

Answer 2

Answer:
`2x-3y=-13`

Explanation:

Standard form of equation of line =
`Ax+by=C` , where A= positive integer and B and C are integers.

The equation of a line that passes through two points (a,b) and (c,d) is given by :-

`(y-b)=(d-b)/(c-a)(x-a)`

Then, the equation of a line that passes through (1, 5) and (-2, 3) will be :-

`(y-5)=(3-5)/(-2-1)(x-1)`

`\Rightarrow\ (y-5)=(-2)/(-3)(x-1)`

`\Rightarrow\ -3(y-5)=-2(x-1)`

`\Rightarrow\ -3(y)-(-3)(5)=-2(x)-(-2)(1)`

`\Rightarrow\ -3y+15=-2x+2` [∵ (-)(-)=(+)]

`\Rightarrow\ 2x-3y=2-15` [Add 2x on both sides and subtract 15 on sides.]

`\Rightarrow\ 2x-3y=-13`

Hence, the standard form of the line that passes through (1, 5) and (-2, 3) :
`2x-3y=-13`