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 point $(2,2)$ and $m = 1$

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 point $(1, - 1)$ and $m = 1$

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 the origin $(0,0)$ and has a slope of 1. Plot the point $(2,2)$ and draw a line with slope 1 passing through it. For $y=x - 2$, the $y$ - intercept is - 2. Plot the point $(1,-1)$ and draw a line with slope 1 passing through it.

Answer:

Graph a line $y=x$ passing through $(2,2)$ and a line $y=x - 2$ passing through $(1,-1)$ on the given coordinate grid.