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

Answer: The value of the y-intercept is $-\frac{3}{5}$

Step-by-step 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 $(0.4,-\frac{1}{2})$ and has a slope of $\frac{1}{4}$. Then we can substitute the following values into  $y=mx+b$:

$x=0.4\\\\y=-\frac{1}{2}\\\\m=\frac{1}{4}$

Then:

$-\frac{1}{2}=\frac{1}{4}(0.4)+b$

And finally, we must solve for "b":

$-\frac{1}{2}=\frac{1}{4}(0.4)+b\\\\-\frac{1}{2}-\frac{1}{10}=b\\\\b=-\frac{3}{5}$

Answer 2

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:

$b = -0.6$