Question

1. slope = \\(\frac{1}{2}\\), through (2, 2)

Explanation:

Step1: Recall Point - Slope Form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m=\frac{1}{2}$ and $(x_1,y_1)=(2,2)$.
Substitute these values into the point - slope formula: $y - 2=\frac{1}{2}(x - 2)$

Step2: Simplify the Equation

Expand the right - hand side: $y - 2=\frac{1}{2}x-1$
Then, add 2 to both sides of the equation to get the slope - intercept form ($y=mx + b$): $y=\frac{1}{2}x-1 + 2=\frac{1}{2}x+1$

Step3: Graph the Line

• The y - intercept is $b = 1$, so the line crosses the y - axis at $(0,1)$.
• Using the slope $m=\frac{1}{2}$, from the point $(0,1)$, we can move up 1 unit and to the right 2 units (or down 1 unit and to the left 2 units) to find other points on the line. Also, we know that the line passes through $(2,2)$. Plot the points $(0,1)$ and $(2,2)$ (and other points found using the slope) and draw a straight line through them.

Answer:

The equation of the line is $y=\frac{1}{2}x + 1$, and to graph it, plot the y - intercept at $(0,1)$ and use the slope $\frac{1}{2}$ (rise 1, run 2) from the point $(0,1)$ or use the point $(2,2)$ along with the slope to draw the line.