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find the slope of the line through each pair of points. 9) (8, 10), (-7…

Question

find the slope of the line through each pair of points.

  1. (8, 10), (-7, 14)
  2. (-3, 1), (-17, 2)
  3. (-20, -4), (-12, -10)
  4. (-12, -5), (0, -8)
  5. (-19, -6), (15, 16)
  6. (-6, 9), (7, -9)
  7. (-18, -20), (-18, -15)
  8. (12, -18), (11, 12)

find the slope of each line.

  1. $y = -5x - 1$
  2. $y = \frac{1}{3}x - 4$
  3. $y = -\frac{1}{5}x - 4$
  4. $x = 1$
  5. $y = \frac{1}{4}x + 1$
  6. $y = -\frac{2}{3}x - 1$
  7. $y = -x + 2$
  8. $y = -x - 1$
  9. $2x + 3y = 9$
  10. $5x + 2y = 6$

Explanation:

Response

Let's solve some of these slope - finding problems. We'll use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) for points \((x_1,y_1)\) and \((x_2,y_2)\), and for linear equations in the form \(y = mx + b\), the slope \(m\) is the coefficient of \(x\). For equations in standard form \(Ax+By = C\), we can rewrite them in slope - intercept form \(y=mx + b\) to find the slope.

Problem 9: Find the slope of the line through \((8,10)\) and \((-7,14)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(8,10)\) and \((x_2,y_2)=(-7,14)\)

Step 2: Apply the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substitute the values: \(m=\frac{14 - 10}{-7 - 8}=\frac{4}{-15}=-\frac{4}{15}\)

Problem 10: Find the slope of the line through \((-3,1)\) and \((-17,2)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(-3,1)\) and \((x_2,y_2)=(-17,2)\)

Step 2: Apply the slope formula

\(m=\frac{2 - 1}{-17-(-3)}=\frac{1}{-17 + 3}=\frac{1}{-14}=-\frac{1}{14}\)

Problem 11: Find the slope of the line through \((-20,-4)\) and \((-12,-10)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(-20,-4)\) and \((x_2,y_2)=(-12,-10)\)

Step 2: Apply the slope formula

\(m=\frac{-10-(-4)}{-12-(-20)}=\frac{-10 + 4}{-12 + 20}=\frac{-6}{8}=-\frac{3}{4}\)

Problem 12: Find the slope of the line through \((-12,-5)\) and \((0,-8)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(-12,-5)\) and \((x_2,y_2)=(0,-8)\)

Step 2: Apply the slope formula

\(m=\frac{-8-(-5)}{0-(-12)}=\frac{-8 + 5}{0 + 12}=\frac{-3}{12}=-\frac{1}{4}\)

Problem 13: Find the slope of the line through \((-19,-6)\) and \((15,16)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(-19,-6)\) and \((x_2,y_2)=(15,16)\)

Step 2: Apply the slope formula

\(m=\frac{16-(-6)}{15-(-19)}=\frac{16 + 6}{15 + 19}=\frac{22}{34}=\frac{11}{17}\)

Problem 14: Find the slope of the line through \((-6,9)\) and \((7,-9)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(-6,9)\) and \((x_2,y_2)=(7,-9)\)

Step 2: Apply the slope formula

\(m=\frac{-9 - 9}{7-(-6)}=\frac{-18}{7 + 6}=\frac{-18}{13}=-\frac{18}{13}\)

Problem 15: Find the slope of the line through \((-18,-20)\) and \((-18,-15)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(-18,-20)\) and \((x_2,y_2)=(-18,-15)\)

Step 2: Apply the slope formula

\(m=\frac{-15-(-20)}{-18-(-18)}=\frac{-15 + 20}{-18 + 18}=\frac{5}{0}\)
Since division by zero is undefined, the slope is undefined (vertical line).

Problem 16: Find the slope of the line through \((12,-18)\) and \((11,12)\)
Step 1: Identify \(x_1,y_1,x_2,y_2\)

Let \((x_1,y_1)=(12,-18)\) and \((x_2,y_2)=(11,12)\)

Step 2: Apply the slope formula

\(m=\frac{12-(-18)}{11 - 12}=\frac{12 + 18}{-1}=\frac{30}{-1}=-30\)

Problem 17: Find the slope of \(y=-5x - 1\)

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Here, the coefficient of \(x\) is \(-5\), so the slope \(m=-5\)

Problem 18: Find the slope of \(y=\frac{1}{3}x-4\)

The equation is in slope - intercept form \(y = mx + b\). The coefficient of \(x\) is \(\frac{1}{3}\), so the slope \(m = \frac{1}{3}\)

Problem 19: Find the slope of \(y=-\frac{1}{5}x-4\)

The equation is in slope - intercept form \(y = mx + b\). The coefficient of \(x\) is \(-\frac{1}{5}\), so the slope \(m=-\frac{1}{5}\)

Problem 20: Find the slope of \(x = 1\)

The line \(x = 1\) is a vertical line. For a vertical line, the slope is undefined (since \(x_2 - x_1=0\) when we us…

Answer:

s:

  1. \(\boldsymbol{-\frac{4}{15}}\)
  2. \(\boldsymbol{-\frac{1}{14}}\)
  3. \(\boldsymbol{-\frac{3}{4}}\)
  4. \(\boldsymbol{-\frac{1}{4}}\)
  5. \(\boldsymbol{\frac{11}{17}}\)
  6. \(\boldsymbol{-\frac{18}{13}}\)
  7. \(\boldsymbol{\text{Undefined}}\)
  8. \(\boldsymbol{-30}\)
  9. \(\boldsymbol{-5}\)
  10. \(\boldsymbol{\frac{1}{3}}\)
  11. \(\boldsymbol{-\frac{1}{5}}\)
  12. \(\boldsymbol{\text{Undefined}}\)
  13. \(\boldsymbol{\frac{1}{4}}\)
  14. \(\boldsymbol{-\frac{2}{3}}\)
  15. \(\boldsymbol{-1}\)
  16. \(\boldsymbol{-1}\)
  17. \(\boldsymbol{-\frac{2}{3}}\)
  18. \(\boldsymbol{-\frac{5}{2}}\)