Question

Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –y equals negative StartFraction one-third EndFraction x plus 9.x + 9 y = –y equals negative StartFraction one-third EndFraction x plus 5.x + 5 y = –3x – 11y y = –3x + 25

Answer 1

B

Explanation:

y=-1/3x+5

Answer 2

`y=-(1)/(3) x+5`

Explanation:

Notice that the answers they give you to choose from are all lines in slope y-intercept form, it would be very simple to just find the answer finding yourself the slope and y-intercept of the line in question.

Since they give you two points
`(x_1,y_1)` and
`(x_2,y_2)` for the line, use them to find the slope of the line that goes through them, with the formula:
`slope=(y_2-y_1)/(x_2-x_1) =(7-6)/(-6-(-3)) =(1)/(-3) =-(1)/(3)`

Therefore, the slope of the line must be
`-(1)/(3)`

Now, find the y-intercept (b) using the general form of a line with the given slope:

`y=-(1)/(3)x +b`

Use one of the given coordinate points to request that the line passes through it. For example, through the point (-3,6) (when x = -3, y must be 6):

`y=-(1)/(3) x+b\\6=-(1)/(3)(-3)+b\\6=1+b\\b=6-1=5`

then the y-intercept must be 5. Therefore our line is :
`y=-(1)/(3)x +5` which appears listed as your second choice.