Question

A line has a slope of 1/4 and passes through point (0.4,-1/2). What is the value of the y-intercept?

Answer 1

For this case we have that by definition, the slope-intersection equation of a line is given by:

`y = mx + b`

Where:

m: It's the slope

y: It is the cut point with the "y" axis

They tell us as data that:

`m = \frac {1} {4}`

So, the equation is:

`y = \frac {1} {4} x + b`

We substitute the given point to find "b":

`- \frac {1} {2} = \frac {1} {4} (0.4) + b\\- \frac {1} {2} = \frac {0.4} {4} + b\\b = - \frac {1} {2} - \frac {0.4} {4}\\b = -0.5-0.1\\b = -0.6`

Thus, the cut point with the y axis is -0.6

Answer:

`b = -0.6`

Answer 2

Answer: The value of the y-intercept is
`-(3)/(5)`

Explanation:

The equation of the line in Slope-intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

In this case we know that the line passes through point
`(0.4,-(1)/(2))` and has a slope of
`(1)/(4)`. Then we can substitute the following values into
`y=mx+b`:

`x=0.4\\\\y=-(1)/(2)\\\\m=(1)/(4)`

Then:

`-(1)/(2)=(1)/(4)(0.4)+b`

And finally, we must solve for "b":

`-(1)/(2)=(1)/(4)(0.4)+b\\\\-(1)/(2)-(1)/(10)=b\\\\b=-(3)/(5)`