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

Answer:

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

Step-by-step 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:

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

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

$\frac{8-b}{a-4} = 2$

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

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

$b = 16-2\cdot a$

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.