Answer:
a. [tex]b=2[/tex]
b. [tex]b = 2a[/tex]
c. [tex]a = \frac{1}{2}b\\[/tex]
d. [tex]b = 10[/tex]
Step-by-step explanation:
Gradient is just another similar term for slope l, [tex]m[/tex], and it can be calculated by [tex]m = \frac{y_2 -y_1}{x_2 -x_1}\\[/tex] where [tex]x_n[/tex] and 1[tex]y_n[/tex] is the [tex]xy[/tex]-coordinates of point [tex]n[/tex]
We let [tex](0,0)[/tex] be point [tex]1[/tex] and [tex](a,b)[/tex] be point [tex]2[/tex], we can then write the equation:
[tex]m = \frac{b -0}{a -0}\\ m = \frac{b}{a}[/tex].
It also says that the points are with a gradient of [tex]2[/tex] so [tex]m = 2[/tex]. We can then write the equation:
[tex]2 = \frac{b}{a}\\[/tex]
Finding [tex]b[/tex]If [tex]a = 1[/tex]:
[tex]2 = \frac{b}{a} \\ 2 = \frac{b}{1} \\ 2 = b \\ b = 2[/tex]
Writing an expression for [tex]b[/tex] in terms of [tex]a[/tex].
[tex]2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{b}{a} \times a = 2 \times a \\ b = 2a[/tex]
Writing an expression for [tex]a[/tex] in terms of [tex]b[/tex]
[tex]2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{a}{b} = \frac{1}{2} \\ \frac{a}{b} \times b = \frac{1}{2} \times b \\ a = \frac{1}{2}b[/tex]
Finding [tex]b[/tex] if [tex]a = 5[/tex]
[tex]2 = \frac{b}{a} \\ 2 = \frac{b}{5} \\ \frac{b}{5} = 2 \\ \frac{b}{5} \times 5 = 2 \times 5 \\ b = 10[/tex]
