Question

What is the slope-intercept form of the equation of the line that passes through the points (2, 7) and (4, −1) ?

y=−4x+12

y=−4x+15

y=−4x+30

y=−4x+3

Answer 1

slope-intercept form ⇒ y = mx + c

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Find slope, m:

$\boxed {\bf{ \text{m = }\dfrac{Y_2 - Y_1}{X_2 - X_1} }}$

$\text {Given } (X_1, Y_1) = (2, 7) \ \ \text {and} \ \ (X_2, Y_2) = (4, -1 ) \ \ ,$

$\text{m = }\dfrac{-1 - 7}{4 - 2} = \dfrac{-8}{2} = -4$

m = -4

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slope-intercept form ⇒ y = -4x + c

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Find y-intercept, c:

Given that it passes through (2, 7),

7 = -4(2) + c

7 = -8 + c

c = 15

.

slope-intercept form ⇒ y = -4x + 15

,

Answer: y = -4x + 15