MATH SOLVE

4 months ago

Q:
# A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = (x – 2). Which equations also represent this line? Check all that apply.y = x – 2y = x + 3y = –5x + 103x + 15y = 305x + 3y = 10

Accepted Solution

A:

slope=(y2-y1)/(x2-x1)=(10-5)/(-4-(-1))=-5/3

Let equation be y=-(5/3)+b => 10=-(5/3)(-4)+b => b=10/3

So the real equation is y=-5/3+10/3 (and not y=x-2)

A. y=x-2 is not equivalent to y=-5/3+10/3

B. y=x+ is not an equation, so cannot be an equivalence

C. 3y = –5x + 10 divide by three => y=-(5/3)+10/3 both slope and y-intercept are equal, so equivalent to y=-5/3+10/3

D. 3x + 15y = 30 divide by 15 => (1/5)x+y = 2 slope and y-intercept are both not equal, so not equivalent to y=-5/3+10/3

E. 5x + 3y = 10 divide by 3 => (5/3)x + y = 10/3 slope and y-intercept are both equal, so equivalent to y=-5/3+10/3

Let equation be y=-(5/3)+b => 10=-(5/3)(-4)+b => b=10/3

So the real equation is y=-5/3+10/3 (and not y=x-2)

A. y=x-2 is not equivalent to y=-5/3+10/3

B. y=x+ is not an equation, so cannot be an equivalence

C. 3y = –5x + 10 divide by three => y=-(5/3)+10/3 both slope and y-intercept are equal, so equivalent to y=-5/3+10/3

D. 3x + 15y = 30 divide by 15 => (1/5)x+y = 2 slope and y-intercept are both not equal, so not equivalent to y=-5/3+10/3

E. 5x + 3y = 10 divide by 3 => (5/3)x + y = 10/3 slope and y-intercept are both equal, so equivalent to y=-5/3+10/3