Question

What is the equation of the line that passes through (0, 3) and (7,0)?

y-ix-3
3
y=x+3
3
y y=-7x+3
y=-x-3

Answer 1

The equation of the line in slope-intercept form is:

`y=-(3)/(7) x+3\\`

In one of the many possible standard forms:

`3\,x+7\,y=21`

Explanation:

First calculate the slope of the segment that joins these two points: (0, 3) and (7,0):

`slope=(y_2-y_1)/(x_2-x_1)= (0-3)/(7-0)=-(3)/(7)`

Now, knowing that the y-intercept is (0, 3) [point on the y-axis (for x=0) where the line crosses], Then the equation of the line in slope-intercept form is:

`y=m\,x+b\\y=-(3)/(7) x+3`

And now, if you want to write the equation eliminating fractions, we can multiply both sides by "7":

`y=-(3)/(7) x+3\\7\,y=-3\,x+21\\3\,x+7\,y=21`