[tex]\begin{gathered} 6)\text{ b = y - mx} \\ 8)\text{ }b\text{ = }\frac{2A\text{ - hc}}{h}\text{ } \end{gathered}[/tex]
Explanation:
6) y = mx + b
We need to make b the subject of the formula:
subtract mx from bith sides:
y - mx = mx - mx + b
y - mx =0 + b
b = y - mx
8) A = 1/2 h(b + c)
We need to make b the subject of formula:
Expand the parenthesis with h:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}(bh\text{ + hc)} \\ \text{Multiply through by 2 as this will cancel the half:} \\ 2A=2\times\frac{1}{2}(bh\text{ + hc)} \\ 2A\text{ = bh + hc} \end{gathered}[/tex][tex]\begin{gathered} \text{subtract hc from both sides:} \\ 2A-\text{ hc = bh + hc - hc} \\ 2A\text{ - hc = bh} \\ \text{divide both sides by h:} \\ \frac{2A\text{ - hc}}{h}\text{ = }\frac{\text{ bh}}{h} \\ b\text{ = }\frac{2A\text{ - hc}}{h}\text{ } \end{gathered}[/tex]
