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-(4)/(5)=(1)/(4)(x-0.2)\Rightarrow y-(4)/(5)=(1)/(4)x-(1)/(4)((2)/(10))\Rightarrow y-(4)/(5)=(1)/(4)x-(1)/(2)((1)/(10))`

Thus, we finally have:

`y-(4)/(5)=(1)/(4)x-(1)/(20)\Rightarrow y=(1)/(4)x-(1)/(20)+(4)/(5)\cdot(4)/(4)\Rightarrow y=(1)/(4)x-(1)/(20)+(16)/(20)=(1)/(4)x+(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=(1)/(4)x_{}+(3)/(4)`