Question

Write the equation of the line in slope intercept form that goes through the points (0,6) and (1,5)

Answer 1

`y=-x+6`

Explanation:

Given: Points (0,6) and (1,5).

Assuming you want the equation in slope intercept form, here's the following step-by-step explanation.

Slope Intercept Form:
`y=mx+b`

1.) Find the slope (m) using the formula:

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

`m = (5-6)/(1-0) = (-1)/(1) = -1`

`m=-1`

2.) Find the y-intercept (b)

We need to isolate
`b` in
`y=mx+b`

To do this, we need to substitute all variables, but
`b`.

To substitute y, We can use either
`y_(2)` or
`y_(1)`.

To substitute x, We can use either
`x_(2)`
`x_(1)`.

To substitute m, We can use the slope in this case, which we found out was 1

For example, we can use the point (0,6)

`6=(-1)(0)+b`

This gives us

`6=0+b\\`

Which finally gives us

`6=b`

We can use the symmetry property of equality (which states if a=b, then b=a) to flip the equation.

That gives us,
`b=6`

Our final answer is,
`y= -x+6`

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