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.


b =

Answer 1

To find the y-intercept \( b \) of the line with a slope \( m = \frac{1}{4} \) that passes through the point \( (0.2, \frac{4}{5}) \), we can use the point-slope form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

Here, \((x_1, y_1) = (0.2, \frac{4}{5})\) and \( m = \frac{1}{4} \).

Substituting the values into the equation:

\[
y - \frac{4}{5} = \frac{1}{4}(x - 0.2)
\]

Now, we will solve for \( y \):

1. Distribute the slope:

\[
y - \frac{4}{5} = \frac{1}{4}x - \frac{1}{4} \cdot 0.2
\]
\[
y - \frac{4}{5} = \frac{1}{4}x - \frac{0.2}{4}
\]
\[
y - \frac{4}{5} = \frac{1}{4}x - 0.05
\]

2. Now add \( \frac{4}{5} \) to both sides to isolate \( y \):

To add \( \frac{4}{5} \) and \(-0.05\), we first convert \( -0.05 \) to a fraction:

\(-0.05 = -\frac{5}{100} = -\frac{1}{20}\).

Now, we find a common denominator:

- The common denominator of \( 5 \) and \( 20 \) is \( 20 \).
- So, convert \( \frac{4}{5} \) to a fraction with a denominator of \( 20 \):

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

Now we can add:

\[
y = \frac{1}{4}x + \left(\frac{16}{20} - \frac{1}{20}\right)
\]
\[
y = \frac{1}{4}x + \frac{15}{20}
\]
\[
y = \frac{1}{4}x + \frac{3}{4}
\]

Now, we can identify the y-intercept \( b \):

\[
b = \frac{3}{4}
\]

Thus, the value of \( b \) is:

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