Question

Write the equation of the line that passes through the points (7, –9)

and (1,-4). Put your answer in fully reduced point-slope form,
unless it is a vertical or horizontal line.

Answer 1

y=
`(-5)/(6)`x+14
`(5)/(6)`

Explanation:

The equation of a line is y=mx+b

to find the equation of the line you need its gradient(m) and its y intercept(b)

the gradient is

`(y1-y2)/(x1-x2)`

y1= the y value of the first point which is -9

y2=the y value of the second point which is -4

x1=the x value of the first point which is 7

x2=the x value of the first point which is 1

then input the values into the equation

`((-9)-(-4))/((7)-(1))`

=
`(-9+4)/(6)`

=
`(-5)/(6)`

to find the y just times the x by the gradient and then minus it from the y

-9-(7 x
`(-5)/(6)`)=14
`(5)/(6)`

making the equation y=
`(-5)/(6)`x+14
`(5)/(6)`