Question

Line passing through points(1.3) and (25)

Answer 1

We need to determine the equation of a line in three forms. The standard expression for this forms can be seen below:

`\begin{gathered} y-y_1=m\cdot(x-x_1)\text{ Point-slope form} \\ y=m\cdot x+b\text{ Slope-intercept form} \\ A\cdot x+B\cdot y=C\text{ Standard form} \end{gathered}`

Where (x1,y1) is a point that belongs to the line, m is the slope and b is the y-intercept. The slope can be calculated with two known points using the following expression:

`m=(y_2-y_1)/(x_2-x_1)`

With this we can find the three equations. To begin we will calculate the slope:

`m=(5-3)/(2-1)=(2)/(1)=2`

Then we can determine the point-slope form using the point (1,3).

`y-3=2\cdot(x-1)`

To determine the slope-intercept form we will use the form above and isolate the y variable on the left side.

`\begin{gathered} y-3=2\cdot(x-1) \\ y=2\cdot x-2+3 \\ y=2\cdot x+1 \end{gathered}`

Finally we can determine the standard form by isolating the constant on the right side.

`\begin{gathered} y=2\cdot x+1 \\ 2\cdot x-y+1=0 \\ 2\cdot x-y=-1 \end{gathered}`