Answer:
The values of [tex]a[/tex] and [tex]b[/tex] are 6 and 4, respectively.
Step-by-step explanation:
Geometrically speaking, any line is represented by equation of the form:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
In addition, the slope is defined in terms of distinct known points. That is:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (2)
If we know that [tex](x_{1},y_{1})=(4,b)[/tex], [tex](x_{2}, y_{2}) = (a, 8)[/tex] and [tex]m = 2[/tex], then the slope is:
[tex]\frac{8-b}{a-4} = 2[/tex]
[tex]8-b = 2\cdot (a-4)[/tex]
[tex]8-b = 2\cdot a -8[/tex]
[tex]b = 16-2\cdot a[/tex]
There is more than one option. If we assume that [tex]a = 6[/tex], then [tex]b[/tex] is:
[tex]b = 16-2\cdot (6)[/tex]
[tex]b = 4[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] are 6 and 4, respectively.
