Question

Help me please!!!!!!

Answer 1

Answer:

a. $b=2$

b. $b = 2a$

c. $a = \frac{1}{2}b$

d. $b = 10$

Step-by-step explanation:

Gradient is just another similar term for slope l, $m$, and it can be calculated by $m = \frac{y_2 -y_1}{x_2 -x_1}$ where $x_n$ and 1$y_n$ is the $xy$-coordinates of point $n$

We let $(0,0)$ be point $1$ and $(a,b)$ be point $2$, we can then write the equation:

$m = \frac{b -0}{a -0}\\ m = \frac{b}{a}$.

It also says that the points are with a gradient of $2$ so $m = 2$. We can then write the equation:

$2 = \frac{b}{a}$

Finding $b$If $a = 1$:

$2 = \frac{b}{a} \\ 2 = \frac{b}{1} \\ 2 = b \\ b = 2$

Writing an expression for $b$ in terms of $a$.

$2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{b}{a} \times a = 2 \times a \\ b = 2a$

Writing an expression for $a$ in terms of $b$

$2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{a}{b} = \frac{1}{2} \\ \frac{a}{b} \times b = \frac{1}{2} \times b \\ a = \frac{1}{2}b$

Finding $b$ if $a = 5$

$2 = \frac{b}{a} \\ 2 = \frac{b}{5} \\ \frac{b}{5} = 2 \\ \frac{b}{5} \times 5 = 2 \times 5 \\ b = 10$