Question

Which is an equation of the line that passes through the points (5,2) and (10,-3)?

A. y = x - 3
B. y = x - 8
C. y = -x + 7
D. y = -x + 12

Answer 1

The answer is C

You get this by first finding the slope between the two points
Y2 - Y1
X2 - X1
It gives you 5/-5 which is -1
So you can narrow it down to options C and D

Now you can just substitute into both equations

2 = -(5) + 7
2 = 2

-3 = -(10) + 7
-3 = -3

Since both coordinates work in C then C is the answer

Answer 2

C

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (10, - 3 )

m =
`(-3-2)/(10-5)` =
`(-5)/(5)` = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 2 ), then

2 = - 5 + c ⇒ c = 2 + 5 = 7

y = - x + 7 ← equation of line