Question

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

Answer 1

From the question, we need to find a line with slope (m) = 1/4, and that passes through the point (0.2, 4/5).

We can use, in this case, the Point-Slope Form of the line, that is:

$y-y_1=m(x-x_1)$

Then, we have:

x1 = 0.2

y1 = 4/5

$y-\frac{4}{5}=\frac{1}{4}(x-0.2)\Rightarrow y-\frac{4}{5}=\frac{1}{4}x-\frac{1}{4}(\frac{2}{10})\Rightarrow y-\frac{4}{5}=\frac{1}{4}x-\frac{1}{2}(\frac{1}{10})$

Thus, we finally have:

$y-\frac{4}{5}=\frac{1}{4}x-\frac{1}{20}\Rightarrow y=\frac{1}{4}x-\frac{1}{20}+\frac{4}{5}\cdot\frac{4}{4}\Rightarrow y=\frac{1}{4}x-\frac{1}{20}+\frac{16}{20}=\frac{1}{4}x+\frac{15}{20}$

We multiply the fraction 4/5 by 4/4 (4/4 = 1) to sum fractions with the same denominator because it is easier to do this in this kind of operation.

Then, the final equation is:

$y=\frac{1}{4}x_{}+\frac{3}{4}$