Which equations in point-slope form represent the line that passes through the points \((-7, 5)\) and \((-4, 1)\)?

Choose exactly two correct answers.

A. \(y - 7 = -\frac{3}{4}(x + 5)\)

B. \(y - 5 = -\frac{4}{3}(x + 7)\)

C. \(y + 4 = -\frac{3}{4}(x + 1)\)

D. \(y - 1 = -\frac{4}{3}(x + 4)\)

an easy way to do it is subtituet (-7,5) and (-4,1) into the equations and find out which ones check. remember (x,y)
so A if we try (-7,5) 5-7=-3/4(-7+5) we can immediately see that -2 is not equal to -3/4(-2) so A is wrong
B
if we try (-7,5) 5-5=-4/3(-7+7) 0=-4/3(0) 0=0 so B is correct
C if we try (-7,5) 5+4=-3/4(-7+1) 9=-3/4(-6) 9 is not equal to 18/4 so C is wrong
D
if we try (-7,5) 5-1=-4/3(-7+4) 4=-4/3(-3) 4=12/3 4=4 D is correct
If you wanted to try the second point (-4,1) in B and D B
1-5=-4/3(-4+7) -4=-4/3(3) -4=-12/3 4=4 B is still correct
D
1-1=-4/3(-4+4) 0=-4/3(0) 0=0 D is still correct
so the answers are B and D

Answered by apologiabiology | 2024-06-10

G e n er a l e q u a t i o n f or l in e in s l o p e in t erce pt f or m : y = a x + b T o f in d a an d b s u b s t i t u d e p o in t s ( − 7 , 5 ) ( − 4 , 1 ) in t o e q u a t i o n { 1 = − 4 a + b ∣ ∗− 1 5 = − 7 a + b ​ { − 1 = 4 a − b 5 = − 7 a + b ​ + − − − − A dd i t i o n m e t h o d 4 = − 3 a ∣ : ( − 3 ) a = − 3 4 ​ b = 5 + 7 a = 5 + 7 ∗ ( − 3 4 ​ ) = 5 − 3 28 ​ = − 4 3 1 ​ A n s w er y = − 3 4 ​ x − 4 3 1 ​ C h ec kin g so l u t i o n : y − 5 = − 3 4 ​ ( x + 7 ) y − 5 = − 3 4 ​ x − 3 28 ​ y = − 3 4 ​ x − 3 28 ​ + 5 y = − 3 4 ​ x − 4 3 1 ​ A n s w er : B an d D .

Answered by luana | 2024-06-10

The equations that represent the line passing through the points ( − 7 , 5 ) and ( − 4 , 1 ) are options B and D. Option B is y − 5 = − 3 4 ​ ( x + 7 ) and option D is y − 1 = − 3 4 ​ ( x + 4 ) . Both equations use the correct slope and a point on the line.
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Answered by apologiabiology | 2025-06-17