Question

graph the following linear functions using slope - intercept form.

1. $3x + y = -5$ 2. $-x + 3y = 12$ 3. $2x - 3y = -6$
2. $5x + y = -5$ 5. $-3x + 7y = -21$ 6. $-x + 4y = 8$
3. $x = -3$ 8. $y = 5$ 9. $7x + 2y = -10$

Explanation:

Step1: Rewrite to slope-intercept form ($y=mx+b$)

1. $3x + y = -5$

$y = -3x -5$

2. $-x + 3y = 12$

$3y = x + 12 \implies y = \frac{1}{3}x + 4$

3. $2x - 3y = -6$

$-3y = -2x -6 \implies y = \frac{2}{3}x + 2$

4. $5x + y = -5$

$y = -5x -5$

5. $-3x + 7y = -21$

$7y = 3x -21 \implies y = \frac{3}{7}x -3$

6. $-x + 4y = 8$

$4y = x + 8 \implies y = \frac{1}{4}x + 2$

7. $x = -3$

(Vertical line, undefined slope, no $y$-intercept)

8. $y = 5$

(Horizontal line, slope $m=0$, $y$-intercept $(0,5)$)

9. $7x + 2y = -10$

$2y = -7x -10 \implies y = -\frac{7}{2}x -5$

Step2: Identify key graphing values

Equation	Slope ($m$)	$y$-intercept $(0,b)$	Special Note
2. $y=\frac{1}{3}x+4$	$\frac{1}{3}$	$(0,4)$
3. $y=\frac{2}{3}x+2$	$\frac{2}{3}$	$(0,2)$
4. $y=-5x-5$	$-5$	$(0,-5)$
5. $y=\frac{3}{7}x-3$	$\frac{3}{7}$	$(0,-3)$
6. $y=\frac{1}{4}x+2$	$\frac{1}{4}$	$(0,2)$
7. $x=-3$	Undefined	None	Vertical line through $x=-3$
8. $y=5$	$0$	$(0,5)$	Horizontal line through $y=5$
9. $y=-\frac{7}{2}x-5$	$-\frac{7}{2}$	$(0,-5)$

Step3: Graph each line

1. Plot the $y$-intercept, then use slope ($\frac{\text{rise}}{\text{run}}$) to plot a second point, draw a straight line through the points.
2. For $x=-3$: Draw a vertical line crossing the $x$-axis at $(-3,0)$.
3. For $y=5$: Draw a horizontal line crossing the $y$-axis at $(0,5)$.

Answer:

1. Line with slope $-3$ and $y$-intercept $(0,-5)$
2. Line with slope $\frac{1}{3}$ and $y$-intercept $(0,4)$
3. Line with slope $\frac{2}{3}$ and $y$-intercept $(0,2)$
4. Line with slope $-5$ and $y$-intercept $(0,-5)$
5. Line with slope $\frac{3}{7}$ and $y$-intercept $(0,-3)$
6. Line with slope $\frac{1}{4}$ and $y$-intercept $(0,2)$
7. Vertical line through $x=-3$
8. Horizontal line through $y=5$
9. Line with slope $-\frac{7}{2}$ and $y$-intercept $(0,-5)$

To graph each, plot the intercept and use the slope to find a second point, then connect the points with a straight line (use the special instructions for vertical/horizontal lines).