To write an equation where x varies directly as y , we can use the formula for direct variation:
Formula of Direct Variation
[tex]\[ \boxed{\mathsf{\textcolor{red}{\Large y = kx}}} \][/tex]
1. y= 28 when x= 7
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{28}{7} = 4 \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = 4x}} } \][/tex]
2. y= 30 when x= 8
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{30}{8} = \frac{15}{4} \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = \frac{15}{4}x}} } \][/tex]
3. y= 0.7 when x= 0.4
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{0.7}{0.4} = 1.75 \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = 1.75x}} } \] [/tex]
4. y= 0.8 when x= 0.5
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{0.8}{0.5} = 1.6 \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = 1.6x}} } \][/tex]
5. y= 400 when x= 25
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{400}{25} = 16 \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = 16x}} } \][/tex]
6. y= 63 when x= 81
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{63}{81} = \frac{7}{9} \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = \frac{7}{9}x}} } \][/tex]
7. y= 200 when x= 300
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{200}{300} = \frac{2}{3} \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = \frac{2}{3}x}} } \][/tex]
8. y= 1 when x= 2
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{1}{2} \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = \frac{1}{2}x}} } \][/tex]
9. y= 48 when x= 6
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{48}{6} = 8 \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = 8x}} } \][/tex]
10. y= 10 when x= 24
[tex]\[ \mathsf{ k = \frac{y}{x} = \frac{10}{24} = \frac{5}{12} \quad \Rightarrow \quad \boxed{\textcolor{brown}{y = \frac{5}{12}x}} } \][/tex]
