Question

Which equation best represents the relationship between x andy in the graph?

Answer 1

the graph is a line, so the general equation of a line is

`y=mx+b`

where m is the slope and b is the y-intercept(when the line touches the y-axis)

Y-intercept

from the graph we can notices the number on y-axis when the line touches it, is

`-3`

then b=-3

now we replace b on the general equation

`y=mx-3`

Slope

we can replace a point of the graph different to the y-intercept n this case I will use (-4,0)

then replace on general equation

`(0)=m(-4)-3`

simplify and solve for m

`\begin{gathered} 0=-4m-3 \\ 3=-4m \\ m=-(3)/(4) \end{gathered}`

the slope is -3/4

Finally

we replace b and the slope on the general equation to find the line

`y=-(3)/(4)x-3`