Question

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Which line has an equation of y=-5x+4 in slope-intercept form?
VX
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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Answer 1

Option B

slope:-

`\\ \sf\longmapsto m= (-24+14)/(4-2)=(-10)/(2)=-5`

Equation of line in point slope form

`\\ \sf\longmapsto y-y_1=m(x-x_1)`

`\\ \sf\longmapsto y+14=-5(x-2)`

`\\ \sf\longmapsto y+14=-5x+10`

`\\ \sf\longmapsto y=-5x+4`

Answer 2

• Option B is close but has different y-intercept

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