Question

1. (-6,2),( , )

graph each line.

1. y = x + 2
2. y = \frac{1}{2}x - 1
3. y - 3 = \frac{1}{3}(x - 3)
4. y + 4 = (x - 5)

Explanation:

Step1: Find the y - intercept

For a linear equation in the form $y=mx + b$ (slope - intercept form), $b$ is the y - intercept. For equations in point - slope form $y - y_1=m(x - x_1)$, we can rewrite them in slope - intercept form.

Step2: Find the slope

The coefficient of $x$ in the slope - intercept form $y=mx + b$ is the slope $m$.

Step3: Plot points

Use the y - intercept as one point $(0,b)$ and use the slope to find other points. If the slope $m=\frac{\text{rise}}{\text{run}}$, from the y - intercept, we can move according to the rise and run to get more points. Then draw a straight line through the points.

For $y = x+2$:

• The slope $m = 1=\frac{1}{1}$ and the y - intercept $b = 2$. So one point is $(0,2)$. Using the slope, if we move 1 unit to the right (run = 1) and 1 unit up (rise = 1), we get the point $(1,3)$. Plot $(0,2)$ and $(1,3)$ and draw a line.

For $y=\frac{1}{2}x - 1$:

• The slope $m=\frac{1}{2}$ and the y - intercept $b=-1$. One point is $(0, - 1)$. Moving 2 units to the right (run = 2) and 1 unit up (rise = 1), we get the point $(2,0)$. Plot $(0,-1)$ and $(2,0)$ and draw a line.

For $y - 3=\frac{1}{3}(x - 3)$:

Rewrite it in slope - intercept form:
$y-3=\frac{1}{3}x - 1$
$y=\frac{1}{3}x+2$
The slope $m = \frac{1}{3}$ and the y - intercept $b = 2$. One point is $(0,2)$. Moving 3 units to the right (run = 3) and 1 unit up (rise = 1), we get the point $(3,3)$. Plot $(0,2)$ and $(3,3)$ and draw a line.

For $y + 4=(x - 5)$:

Rewrite it in slope - intercept form:
$y=x-9$
The slope $m = 1$ and the y - intercept $b=-9$. One point is $(0,-9)$. Moving 1 unit to the right (run = 1) and 1 unit up (rise = 1), we get the point $(1,-8)$. Plot $(0,-9)$ and $(1,-8)$ and draw a line.

To graph each line, follow the above - described point - plotting and line - drawing process for each equation.

Answer:

Step1: Find the y - intercept

For a linear equation in the form $y=mx + b$ (slope - intercept form), $b$ is the y - intercept. For equations in point - slope form $y - y_1=m(x - x_1)$, we can rewrite them in slope - intercept form.

Step2: Find the slope

The coefficient of $x$ in the slope - intercept form $y=mx + b$ is the slope $m$.

Step3: Plot points

Use the y - intercept as one point $(0,b)$ and use the slope to find other points. If the slope $m=\frac{\text{rise}}{\text{run}}$, from the y - intercept, we can move according to the rise and run to get more points. Then draw a straight line through the points.

For $y = x+2$:

• The slope $m = 1=\frac{1}{1}$ and the y - intercept $b = 2$. So one point is $(0,2)$. Using the slope, if we move 1 unit to the right (run = 1) and 1 unit up (rise = 1), we get the point $(1,3)$. Plot $(0,2)$ and $(1,3)$ and draw a line.

For $y=\frac{1}{2}x - 1$:

• The slope $m=\frac{1}{2}$ and the y - intercept $b=-1$. One point is $(0, - 1)$. Moving 2 units to the right (run = 2) and 1 unit up (rise = 1), we get the point $(2,0)$. Plot $(0,-1)$ and $(2,0)$ and draw a line.

For $y - 3=\frac{1}{3}(x - 3)$:

Rewrite it in slope - intercept form:
$y-3=\frac{1}{3}x - 1$
$y=\frac{1}{3}x+2$
The slope $m = \frac{1}{3}$ and the y - intercept $b = 2$. One point is $(0,2)$. Moving 3 units to the right (run = 3) and 1 unit up (rise = 1), we get the point $(3,3)$. Plot $(0,2)$ and $(3,3)$ and draw a line.

For $y + 4=(x - 5)$:

Rewrite it in slope - intercept form:
$y=x-9$
The slope $m = 1$ and the y - intercept $b=-9$. One point is $(0,-9)$. Moving 1 unit to the right (run = 1) and 1 unit up (rise = 1), we get the point $(1,-8)$. Plot $(0,-9)$ and $(1,-8)$ and draw a line.

To graph each line, follow the above - described point - plotting and line - drawing process for each equation.