Answers:
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1) " y = - x – 5 " .
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2) " y = -2x + 2 "
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3) y = " [tex] \frac{7}{4} [/tex] x + [tex] \frac{11}{4} [/tex] " .
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Explanation:
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1) " y = -x – 5 " .
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = -1 " ;
the y-intercept, "b = -5 " .
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1) y = -x – 5 ;
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = -1 " ;
the y-intercept, "b = -5 " .
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2) " y = -2x + 2 " .
Note: Given: "(x₁, y₁)" ; that is: "(-2, 6)" ; in which: "x₁ = -2" ; and: "y₁ =6" ;
And given the slope, "m", = -2 ;
Use the formula:
" y – y₁ = m(x – x₁) " ;
And substitute our known values:
" y – 6 = -2 [x – (-2)] " ;
→ " y – 6 = -2 (x + 2) ;
→ " y – 6 = (-2*x) + (-2*2) ;
→ " y – 6 = (-2*x) + (-2*2) ;
→ " y – 6 = -2x + (-4) ;
→ " y – 6 = -2x – 4 ;
→ Now, add "6" to EACH SIDE of the equation; to isolate "y" on the
"left-hand side" of the equation; & write in "slope-intercept form" ;
→ " y – 6 + 6 = -2x – 4 + 6 ;
to get:
→ " y = -2x + 2 " .
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = -2 " ;
the y-intercept, "b = 2 " .
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3) " y = [tex] \frac{7}{4} [/tex] x + [tex] \frac{11}{4} [/tex] " .
Given the points: "(-1, 1)" ; and "(7, 15):
→ "(x₁, y₁)" ↔ "(-1, 1)" ; in which: " x₁ = -1 " ; " y₁ = 1 " ;
→ "(x₂ , y₂)" ↔ "(7, 15)" ; in which: " x₂ = 7 " ; "y₂ = 15 " ;
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Calculate the slope, "m" :
→ m = (y₂ – y₁) / (x₂ – x₁) ;
= (15 – 1) / [ 7 – (-1) ] = (15 – 1) / ( 7 + 1) ;
= [tex] \frac{14}{8} = \frac{(14/2)}{(8/2)} = \frac{7}{4} [/tex] ;
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→ Now, use the formula:
→ " y – y₁ = m(x – x₁) " ;
And substitute our known values:
→ " y – 1 = [tex] \frac{7}{4} [/tex] [x – (-1)] " ;
→ " y – 1 = [tex] \frac{7}{4} [/tex] (x + 1) " ;
→ " y – 1 = [tex] \frac{7}{4} [/tex] x + [tex] \frac{7}{4} [/tex] " ;
→ Now, add "1" to EACH SIDE of the equation; to isolate "y" on the
"left-hand side" of the equation; & write in "slope-intercept form" ;
→ " y – 1 + 1 = [tex] \frac{7}{4} [/tex] x + [tex] \frac{7}{4} [/tex] + 1 " ;
to get:
→ " y = [tex] \frac{7}{4} [/tex] x + [tex] \frac{11}{4} [/tex] " .
And substitute our known values:
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = [tex] \frac{7}{4} [/tex] " ;
the y-intercept, "b = [tex] \frac{11}{4} [/tex] " .
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