Question

Cora says he dosen't need to know the y-interce of a line to write its equation,just its slope and some other point on the line.Is she correct? Explain. If Cora is correct,explain how to find the equation of a line with a slope of -1/3 that includes the point (2,6)

Answer 1

Yes, Cora is correct.

The equation of line with point (2,6) and slope of line (-1/3)

is x + 3y - 20 = 0

Explanation:

Yes, the equation of a line can be written using a point and a slope of the line equation.

Cora has used the POINT SLOPE FORMULA, to represent the line equation.

In Point Slope formula:

The equation with slope m and points (x0,y0) can be written as:

(y-y0) =m (x-x0)

Here, the point (x0,y0) = (2,6)

and slope m = (-1/3)

So, the equation can be written as:
`( y - 6) =(-1)/(3) (x-2) \\\implies 3( y-6) = (2-x)\\or, 3y - 18 -2 + x = 0\\or, x + 3y - 20 = 0`

Hence, the equation of line with point (2,6) and slope of line (-1/3)

is x + 3y - 20 = 0