Question

draw a line through the point (2, 2) with a slope of 1. draw a line through the point (1, - 1) with a slope of 1

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: For the point $(2,2)$ and slope $m = 1$

Substitute $x_1 = 2$, $y_1=2$ and $m = 1$ into the point - slope form: $y - 2=1\times(x - 2)$, which simplifies to $y=x$.

Step3: For the point $(1,-1)$ and slope $m = 1$

Substitute $x_1 = 1$, $y_1=-1$ and $m = 1$ into the point - slope form: $y+1 = 1\times(x - 1)$, which simplifies to $y=x - 2$.

Step4: Graph the lines

For $y=x$, the line passes through points like $(0,0)$, $(1,1)$, $(2,2)$ etc. For $y=x - 2$, the line has a $y$ - intercept of $-2$ and passes through points like $(0,-2)$, $(1,-1)$, $(2,0)$ etc.

Answer:

To draw the line through $(2,2)$ with slope 1, start at the point $(2,2)$ and since the slope is 1 (rise 1, run 1), you can find other points by moving 1 unit up and 1 unit to the right or 1 unit down and 1 unit to the left. For the line through $(1,-1)$ with slope 1, start at $(1,-1)$ and again use the rise - run property (rise 1, run 1) to find additional points and draw the line.