Question

What is the equation that passes through (4, 3) and (2, -1)?

Y = 2x - 5

y = 4x -13

y = 6x+4

y = 1/2 x -2

Answer 1

Answer: first option.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

To find "m", we need to substitute the coordinates of the points (4, 3) and (2, -1) into this formula:

`m=(y_2-y_1)/(x_2-x_1)`

We can identify that:

`y_2=-1\\y_1=3\\x_2=2\\x_1=4`

Then:

`m=(-1-3)/(2-4)\\\\m=2`

To find "b" we must substitute the slope and one of the given points into
`y=mx+b` and solve for "b". Then, this is:

`3=2(4)+b\\\\3-8=b\\\\b=-5`

Therefore, the equation of this line is:

`y=2x-5`

Answer 2

y = 2x - 5

Explanation:

We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).

Finding the slope:

Slope =
`(3-(-1))/(4-2) =2`

Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.

`y=mx+c`

`-1 = 2 (2) + c \\\\ c = - 5`

So the equation of the line would be
`y=2x-5`