Question

Need help quick.

1. Write the standard form of the line that contains a slope of 1/2 and y -intercept of 3. Include your work in your final answer.
2. Write the standard form of the line that passes through the given points.
(-1, -3) and (2, 1)

Answer 1

Hello there,

1. The standard form of a straight line with a slope and a y-intercept is as follows:

`y=mx+b`, where
`m` is the slope and
`b` is the y-intercept.

In this case, we have a slope of
`(1)/(2)` and a y-intercept of 3. Plugging in
`(1)/(2)` for
`m` and 3 for
`b` gives us:

`y=(1)/(2)x+3`

2. We are given two points. With these two points, we can find the slope with the formula for the slope to be:

`m=(y_(2)-y_(1) )/(x_(2)-x_(1))`

We can use the points and the corresponding values to solve for the slope:

`m=(1-(-3))/(2-(-1))=(4)/(3)`

We can plug
`m` into our equation:

`y=(4)/(3)x+b`

To find b, we simply plug in one of our points into this equation, and solve. I will use (2, 1) since both values are positive, but feel free to use (-1, -3) if you'd like:

`1=(4)/(3)(2)+b`

`1=(8)/(3)+b`

`-(5)/(3)=b`

Now plug
`b` into the equation.

`y=(4)/(3)x-(5)/(3)`

Hope this helps! :^)