Question

I need HELP, I'm just a dumb kid from Minnesota, I have no clue what to do...The line below has a slope of 2. Both points are on the same line. Find the values of a and b

Answer 1

The values of
`a` and
`b` are 6 and 4, respectively.

Explanation:

Geometrically speaking, any line is represented by equation of the form:

`y = m\cdot x + b` (1)

Where:

`x` - Independent variable, dimensionless.

`y` - Dependent variable, dimensionless.

`m` - Slope, dimensionless.

`b` - y-Intercept, dimensionless.

In addition, the slope is defined in terms of distinct known points. That is:

`m = (y_(2)-y_(1))/(x_(2)-x_(1))` (2)

If we know that
`(x_(1),y_(1))=(4,b)`,
`(x_(2), y_(2)) = (a, 8)` and
`m = 2`, then the slope is:

`(8-b)/(a-4) = 2`

`8-b = 2\cdot (a-4)`

`8-b = 2\cdot a -8`

`b = 16-2\cdot a`

There is more than one option. If we assume that
`a = 6`, then
`b` is:

`b = 16-2\cdot (6)`

`b = 4`

The values of
`a` and
`b` are 6 and 4, respectively.