Question

part - a
find the equation of the line with the given slope and the y - intercept.

1. slope = -3 ; y - intercept = 4 2) slope = -1 ; y - intercept = 0
2. slope = \\(\frac{1}{5}\\) ; y - intercept = -5 4) slope = 2 ; y - intercept = -9
3. slope = -8 ; y - intercept = 8 6) slope = -4 ; y - intercept = \\(-\frac{7}{2}\\)
4. slope = 9 ; y - intercept = 2 8) slope = 5 ; y - intercept = -1

part - b

1. if a line cuts the y - axis at y = -6 and the slope of the line is -10, find the equation of the line.
2. find the equation of the tangent whose slope is 3 and has the y - intercept 1.

Explanation:

Step1: Recall slope-intercept form

The slope-intercept equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

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Part A

Step2: Substitute values for 1)

Substitute $m=-3$, $b=4$:
$y = -3x + 4$

Step3: Substitute values for 2)

Substitute $m=-1$, $b=0$:
$y = -1x + 0$ or $y = -x$

Step4: Substitute values for 3)

Substitute $m=\frac{1}{5}$, $b=-5$:
$y = \frac{1}{5}x - 5$

Step5: Substitute values for 4)

Substitute $m=2$, $b=-9$:
$y = 2x - 9$

Step6: Substitute values for 5)

Substitute $m=-8$, $b=8$:
$y = -8x + 8$

Step7: Substitute values for 6)

Substitute $m=-4$, $b=-\frac{7}{2}$:
$y = -4x - \frac{7}{2}$

Step8: Substitute values for 7)

Substitute $m=9$, $b=2$:
$y = 9x + 2$

Step9: Substitute values for 8)

Substitute $m=5$, $b=-1$:
$y = 5x - 1$

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Part B

Step10: Solve Part B 1)

y-intercept $b=-6$, slope $m=-10$:
$y = -10x - 6$

Step11: Solve Part B 2)

Substitute $m=3$, $b=1$:
$y = 3x + 1$

Answer:

Part A

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

Part B

1. $y = -10x - 6$
2. $y = 3x + 1$