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

Answer:

x - 6y = -9

Step-by-step explanation:

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

Slope ($m$) = $\frac{2-1}{3+3} =\frac{1}{6}$

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).

$2=\frac{1}{6} +c\\\\c=\frac{3}{2}$

So the equation of the line which passes through the given points will be $y=\frac{1}{6} x+\frac{3}{2}$ which can be rearranged to write it as:

x - 6y = -9

Answer 2

Answer:

Option C.

Step-by-step explanation:

The standard form of a line is

$Ax+By=C$

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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-(1)=\dfrac{2-1}{3-(-3)}(x-(-3))$

$y-1=\dfrac{1}{6}(x+3)$

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.