Question

Sarita says the equation of a line with a y-intercept of 7 that includes the point (3, -2) is y = -2 / 3 x + 7. Is she right? If so, explain why. If not, find the correct equation.

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: Is the slope

b: Is the cut-off point with the y axis

According to the data of the statement we have two points through which the line passes:

`(x_ {1}, y_ {1}): (0,7)`(The cut-off point "b" is 7)

`(x_ {2}, y_ {2}): (3, -2)`

We found the slope:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-7} {3-0} = \frac {-9} {3} = -3`

Thus, the equation is of the form:

`y = -3x + b`

We know that
`b = 7`

Finally, the equation is:

`y = -3x + 7`

So, Sarita is not right.

Answer:

`y = -3x + 7`