Question

cora says she doesn't need to know the y-intercept 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 alope of -1/3 that includes the point (2,6).​

Answer 1

Answer:

The equation of line with given slope that include given points is                 3 y + x - 20 = 0

Step-by-step explanation:

According to Cora , if we know the slope and points on a line then we can write the equation of a line .

Since , The equation of line in slope-intercept form is

y = m x + c

Where m is the slope of line , and if we know the points ( x , y ) which satisfy the line then constant term c can be get and the equation of line can be formed .

So , From the statement said above it is clear that she is correct .

Now , Again

Given as :

Slope of a line is m = - $\frac{1}{3}$

That include points ( 2 , 6 )

Now from the equation of line as  y = m x + c

∴   6 =  - $\frac{1}{3}$ ( 2 ) + c

Or, 6 =  - $\frac{2}{3}$  + c

So , c = 6 + $\frac{2}{3}$

or,  c = $\frac{18 + 2}{3}$

∴   c = $\frac{20}{3}$

So, The equation of line can be written as

 y =   - $\frac{1}{3}$ x + $\frac{20}{3}$

Or, 3 y = - x + 20

I.e  3 y + x - 20 = 0

Hence The equation of line with given slope that include given points is     3 y + x - 20 = 0   Answer