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

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

[tex]2=\frac{1}{6} +c\\\\c=\frac{3}{2}[/tex]

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

x - 6y = -9

erinna erinna · Answer 2 · 2019-12-22T05:41:29+01:00

Answer:

Option C.

Step-by-step explanation:

The standard form of a line is

[tex]Ax+By=C[/tex]

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

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

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

[tex]y-(1)=\dfrac{2-1}{3-(-3)}(x-(-3))[/tex]

[tex]y-1=\dfrac{1}{6}(x+3)[/tex]

Multiply both sides by 6.

[tex]6(y-1)=x+3[/tex]

[tex]6y-6=x+3[/tex]

Subtract 6y and 3 from both sides.

[tex]6y-6-6y-3=x+3-6y-3[/tex]

[tex]-6-3=x-6y[/tex]

[tex]-9=x-6y[/tex]

Interchange both sides.

[tex]x-6y=-9[/tex]

Therefore, the correct option is C.