Question

Write the standard form of the equation of the line through the given points.

Through: (0,1) and (1,2)

Answer 1

`\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-1}{1-0}\implies \cfrac{1}{1}\implies 1 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-1=1(x-0)\implies y-1=x \\\\\\ \stackrel{standard~form}{-x+y=1}`

Answer 2

Hello!

First we find the slope, which is the the difference of the y-values divided by the difference of the x-values as seen below.


`(2-1)/(1-0) = (1)/(1)= 1`

The slope of our line is 1.

Now, the y-intercept is where x=0 is located at. As you can see, we already have a point with x=0. Therefore our y-intercept is 1, as the y-value is in that ordered pair.

Just to check, we will plug in a point from our line (1,2) in the slope intercept equation and solve for b.

2=1(1)+b
2=1+b
b=1

We can write our equation in standard form (Ax+By=C) below.

-x+y=1

I hope this helps!