Question

What is the equation of the line in standard form? A function graph of a line with two points (-3,1) and (3,2) with an x axis of negative five to five and a y axis of negative five to five x + 6y = 9 3x + y = 6 x−6y=−9 3x−y=−6

Answer 1

Option C.

Explanation:

The standard form of a line is

`Ax+By=C`

It a line passes through two points then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

It is given that the line passes through the points (-3,1) and (3,2). So the equation of line is

`y-(1)=(2-1)/(3-(-3))(x-(-3))`

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

Multiply both sides by 6.

`6(y-1)=x+3`

`6y-6=x+3`

Subtract 6y and 3 from both sides.

`6y-6-6y-3=x+3-6y-3`

`-6-3=x-6y`

`-9=x-6y`

Interchange both sides.

`x-6y=-9`

Therefore, the correct option is C.

Answer 2

x - 6y = -9

Explanation:

We are given two points (-3,1) and (3,2) on a line so we will use them to find the slope.

Slope (
`m`) =
`(2-1)/(3+3) =(1)/(6)`

The standard form of the equation is
`y=mx+c` so we will substitute the values of the coordinates of a point and slope (m) to find the y-intercept (c).

`2=(1)/(6) +c\\\\c=(3)/(2)`

So the equation of the line which passes through the given points will be
`y=(1)/(6) x+(3)/(2)` which can be rearranged to write it as:

x - 6y = -9