Question

What is the equation of the straight line that passes through the points (0,3) and (4,3)

Answer 1

`y=3`

Explanation:

The slope of a line is given as
`m=(\Delta y)/(\Delta x)`, where
`\Delta y` is change in y-value and
`\Delta x` is change in x-value for any two points the line passes through.

Using the points (0, 3) and (4, 3) as given in the problem, we have:

`m=(0)/(-4)=0`. Therefore, the slope of this line is 0.

In slope-intercept form, we have
`y=mx+b`. Since we've found out that
`m=0` the entire term
`mx` will be equal to 0 and we are left with
`y=b`, where
`b` is the y-intercept. We can plug in the coordinates of any point the line passes through to find this value:

Using the point (4, 3) as given in the problem:

`3=0(4)+b,\\3=0+b,\\b=3`

Thus, the equation of our line is
`y=0x+3,\\\boxed{y=3}`