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Which line has an equation of y=-5x+4 in slope-intercept form?
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O a line passing through the points (1,9) and (3, 19)
a line passing through the points (2, -14) and (4, -24)
O a line passing through the points (1, 1) and (3, 11)
O a line passing through the points (2,6) and (4, -16)
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Sagot :

Option B

slope:-

[tex]\\ \sf\longmapsto m= \dfrac{-24+14}{4-2}=\dfrac{-10}{2}=-5[/tex]

Equation of line in point slope form

[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]

[tex]\\ \sf\longmapsto y+14=-5(x-2)[/tex]

[tex]\\ \sf\longmapsto y+14=-5x+10[/tex]

[tex]\\ \sf\longmapsto y=-5x+4[/tex]

mhanifa

Answer:

  • Option B is close but has different y-intercept

Step-by-step explanation:

Let's verify each line for their slope, we are looking for m = - 5

A. a line passing through the points (1,9) and (3, 19)

  • m = (19 - 9)/(3 - 1) = 10/2 = 5, no

B. a line passing through the points (2, -14) and (4, -24)

  • m = (-24 + 14)/(4 - 2) = -10/2 = - 5

The slope is correct, find the y-intercept:

  • -14 = -5*2 + b
  • -14 + 10 = b
  • -4 = b

The line is:

  • y = - 5x - 4

The line has same slope but different y-intercept

C. a line passing through the points (1, 1) and (3, 11)

  • m = (11 - 1)/(3 - 1) = 10/2 = 5, no

D. a line passing through the points (2,6) and (4, -16)

  • m = (-16 - 6)/(4 - 2) = -22/2 = - 11, no
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