Question

Write the equation of the line passing through the points (0.1,-1.6) and (3,7.7),Please write the line in slope intercept form

Answer 1

The line can be expressed in slope intercept form in the following manner:

`y(x)\text{ = m}\cdot x\text{ + b}`

Where "m" is the slope and "b" is the y-intercept. We need at least two known points to find the expression. The expression of the slope is given by:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

Applying the known points (0.1, -1.6) and (3, 7.7).

`\begin{gathered} m\text{ = }\frac{7.7\text{ - (-1.6)}}{3\text{ - 0.1}} \\ m\text{ = }\frac{7.7\text{ + 1.6}}{2.9} \\ m\text{ = }(9.3)/(2.9) \\ m\text{ = }3.21 \end{gathered}`

The expression of the line thus far is:

`y(x)\text{ = 3.21}\cdot x\text{ + b}`

We need to find the value of "b", to do that we need to apply one of the known points:

`\begin{gathered} -1.6=3.21\cdot0.1+b \\ -1.6=0.321+b \\ b=-1.6-0.321 \\ b=-1.921 \end{gathered}`

We now have the whole expression of the line:

`y(x)=3.21\cdot x-1.921`