Question

Which equation below represents a line with a slope of - 2/3 that passes through the point (-4.5 , 10)?

A. y = - 2/3 x + 10
B. y = - 2/3 x +2.7
C. y = - 2/3 x + 7
D. y = - 2/3 x + 13

pls explain the answer if possible ^^​

Answer 1

Option C

Explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.

Let's try this with option C. To make things easier, convert -4.5 into decimal form:
`-4(1)/(2)`. Substitute
`-4(1)/(2)` for x and 10 for y in the equation, then solve:

`y = -(2)/(3) x+7\\\\10 = -(2)/(3) (-4(1)/(2) )+7\\10 = -(2)/(3) (-(9)/(2))+7\\10 = 3+7\\10 = 10`

10 does equal 10, so this is a true statement. Option C is the right answer.