Question

Which equation represents the line that passes through (-6, 7) and (-3, 6)?

y=-3x+9
y=-x+5
y=-3x - 117
y = -3x + 25

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points through which the line passes:

`(x_ {1}, y_ {1}): (- 6,7)\\(x_ {2}, y_ {2}): (- 3,6)`

We find the slope of the line:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {6-7} {- 3 - (- 6)} = \frac {-1} {-3 + 6} = \frac {-1} {3} = -\frac {1} {3}`

Thus, the equation of the line is of the form:

`y = - \frac {1} {3} x + b`

We substitute one of the points and find b:

`6 = - \frac {1} {3} (- 3) + b\\6 = 1 + b\\b = 5`

Finally, the equation is:

`y = - \frac {1} {3} x + 5`

Answer:

`y = - \frac {1} {3} x + 5`