Question

Graph the line through point (1,1) with slope 2.

Answer 1

Step-by-step explanation:

The equation of a line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$ intercept.

We know that the line pass through the point (1,1) and the slope is 2.

$m=2$

Then,

$y=2x+b$

We have to find $b$.

If we replace the point (1,1) in $y=2x+b$ we will obtain $b$.

Then,

$y=2x+b\\1=2.1+b\\1=2+b\\1-2=b\\-1=b$

$y=2x-1$

The y intercept then is -1, this means that when x=0, y=-1.

We have the point (0,-1).

Now to obtain another point we have to replace  $y=2x-1$ with y=0.

$y=2x-1\\0=2x-1\\1=2x\\\frac{1}{2}=x$

We have the point $(\frac{1}{2},0)=(0.5,0)$

Now that we have to points, we have to place them in the cartesian coordinate system. And then draw the line.