Question

write an equation in slope-intercept form for the given points.
1.
points: (0, 1), (3, -2)
2.
points: (0, -4), (1, 1)
3.
points: (-3, -3), (0, -2)
4.

x	y
-4	1
-2	-3
0	-7
2	-11

5.

x	y
-6	-1
-3	1
0	3
3	5

6.

x	y
-4	0
-2	2
0	4
2	6

write an equation of the line that passes through the given points.

1. (0, 0), (3, -9)
2. (-2, 5), (0, 5)
3. (-4, 3), (0, 5)

Explanation:

1.

Step1: Identify slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$
Use points $(0,1)$ and $(3,-2)$:
$m = \frac{-2 - 1}{3 - 0} = \frac{-3}{3} = -1$

Step2: Identify y-intercept

$b = 1$ (from point $(0,1)$)

Step3: Write slope-intercept form

$y = mx + b$
$y = -1x + 1$

2.

Step1: Calculate slope

Use points $(0,-4)$ and $(1,1)$:
$m = \frac{1 - (-4)}{1 - 0} = \frac{5}{1} = 5$

Step2: Identify y-intercept

$b = -4$ (from point $(0,-4)$)

Step3: Write equation

$y = 5x - 4$

3.

Step1: Calculate slope

Use points $(0,-2)$ and $(-3,-3)$:
$m = \frac{-3 - (-2)}{-3 - 0} = \frac{-1}{-3} = \frac{1}{3}$

Step2: Identify y-intercept

$b = -2$ (from point $(0,-2)$)

Step3: Write equation

$y = \frac{1}{3}x - 2$

4.

Step1: Calculate slope

Use points $(0,-7)$ and $(-4,1)$:
$m = \frac{1 - (-7)}{-4 - 0} = \frac{8}{-4} = -2$

Step2: Identify y-intercept

$b = -7$ (from point $(0,-7)$)

Step3: Write equation

$y = -2x - 7$

5.

Step1: Calculate slope

Use points $(0,3)$ and $(-6,-1)$:
$m = \frac{-1 - 3}{-6 - 0} = \frac{-4}{-6} = \frac{2}{3}$

Step2: Identify y-intercept

$b = 3$ (from point $(0,3)$)

Step3: Write equation

$y = \frac{2}{3}x + 3$

6.

Step1: Calculate slope

Use points $(0,4)$ and $(-4,0)$:
$m = \frac{0 - 4}{-4 - 0} = \frac{-4}{-4} = 1$

Step2: Identify y-intercept

$b = 4$ (from point $(0,4)$)

Step3: Write equation

$y = x + 4$

7.

Step1: Calculate slope

Use points $(0,0)$ and $(3,-9)$:
$m = \frac{-9 - 0}{3 - 0} = \frac{-9}{3} = -3$

Step2: Identify y-intercept

$b = 0$ (from point $(0,0)$)

Step3: Write equation

$y = -3x$

8.

Step1: Calculate slope

Use points $(0,5)$ and $(-2,5)$:
$m = \frac{5 - 5}{-2 - 0} = \frac{0}{-2} = 0$

Step2: Identify y-intercept

$b = 5$ (from point $(0,5)$)

Step3: Write equation

$y = 0x + 5 = 5$

9.

Step1: Calculate slope

Use points $(0,5)$ and $(-4,3)$:
$m = \frac{3 - 5}{-4 - 0} = \frac{-2}{-4} = \frac{1}{2}$

Step2: Identify y-intercept

$b = 5$ (from point $(0,5)$)

Step3: Write equation

$y = \frac{1}{2}x + 5$

Answer:

1. $y = -x + 1$
2. $y = 5x - 4$
3. $y = \frac{1}{3}x - 2$
4. $y = -2x - 7$
5. $y = \frac{2}{3}x + 3$
6. $y = x + 4$
7. $y = -3x$
8. $y = 5$
9. $y = \frac{1}{2}x + 5$