Question

Asap answer pls-----------

Answer 1

`y=(4)/(5)x-(18)/(5)`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0).

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where two points on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

In the graph, the points (-3,-6) and (2,-2) are plotted clearly, so we can use these to help us find the slope. Plug them into the equation:

`m=(-6-(-2))/(-3-2)\\m=(-6+2)/(-3-2)\\m=(-4)/(-5)\\m=(4)/(5)`

Therefore, the slope of the line is
`(4)/(5)`. Plug this into
`y=mx+b` :

`y=(4)/(5)x+b`

2) Determine the y-intercept (b)

`y=(4)/(5)x+b`

Typically, given a graph, we could look at where exactly the line crosses the y-axis to determine b. However, because it appears ambiguous on this graph, we must solve it algebraically.

Plug in one of the given points (2,-2) and solve for b:

`-2=(4)/(5)(2)+b\\-2=(8)/(5)+b`

Subtract
`(8)/(5)` from both sides to isolate b

`-2-(8)/(5)=(8)/(5)+b-(8)/(5)\\-(18)/(5) =b`

Therefore, the y-intercept of the line is
`-(18)/(5)`. Plug this back into
`y=(4)/(5)x+b`:

`y=(4)/(5)x+(-(18)/(5))\\y=(4)/(5)x-(18)/(5)`

I hope this helps!