Answer: The slope is [tex]\frac{-2}{5}[/tex] and the y-intercept is [tex]\frac{-1}{3}[/tex]
Step-by-step explanation:
We know that the intercept form of a linear function is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line and c is the y intercept point.
The slope of a function is given by :-
[tex]m=\dfrac{\text{change in y}}{\text{change in x}}\\\\\\\Rightarrow\ m=\dfrac{\frac{-2}{15}-\frac{-1}{30}}{\frac{-1}{2}-\frac{-3}{4}}\\\\\\\Rightarrow\ m=\dfrac{\frac{-3}{30}}{\frac{1}{4}}=\dfrac{-2}{5}[/tex]
Put the value of m in the general intercept equation , we get
[tex]y=\frac{-2}{5}x+c[/tex]
Put [tex]x=\frac{-1}{2}[/tex] and [tex]y=\frac{-2}{15}[/tex] in it , we get
[tex]\frac{-2}{15}=\frac{-2}{5}\times \frac{-1}{2}+c\\\\\Rightarrow\ c=\frac{-2}{15}\times\frac{5}{1}=\frac{-1}{3}[/tex]
Hence, The slope is [tex]\frac{-2}{5}[/tex] and the y-intercept is [tex]\frac{-1}{3}[/tex]
