Question

A line has a slope of
1
4
and passes through the point (0.2,
4
5
).

Find the value of b, the y-intercept.

Answer 1

The equation of a line in slope-intercept form is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. In this case, the slope \(m\) is given as \(\frac{1}{4}\), and the line passes through the point \((0.2, \frac{4}{5})\).

We can substitute the slope and the coordinates of the point into the equation to find \(b\):

1. Substitute \(m = \frac{1}{4}\), \(x = 0.2\), and \(y = \frac{4}{5}\):

\[
\frac{4}{5} = \frac{1}{4}(0.2) + b
\]

2. Calculate \(\frac{1}{4}(0.2)\):

\[
\frac{1}{4}(0.2) = \frac{0.2}{4} = \frac{0.2}{4} = 0.05
\]

3. Now, substituting this value into the equation gives:

\[
\frac{4}{5} = 0.05 + b
\]

4. To find \(b\), we need to isolate it:

\[
b = \frac{4}{5} - 0.05
\]

5. Convert \(0.05\) to a fraction to make the subtraction easier. \(0.05 = \frac{5}{100} = \frac{1}{20}\).

6. Now, we need a common denominator to subtract \(\frac{4}{5}\) and \(\frac{1}{20}\). The common denominator is \(20\):

\[
\frac{4}{5} = \frac{16}{20}
\]

So we have:

\[
b = \frac{16}{20} - \frac{1}{20} = \frac{16 - 1}{20} = \frac{15}{20} = \frac{3}{4}
\]

Thus, the value of \(b\), the y-intercept, is:

\[
\boxed{\frac{3}{4}}
\]