Question

Please help me !!

Line q goes through points (-3, 3) and (-5, -3). At what point does line q cross the y-axis?

Answer 1

It crosses the y-axis at the point where y = 12

- the point (0, 12).

Explanation:

First we need to find the equation of the line q:

The slope of the line = (-3-3)/(-5-(-3))

= -6/-2

= 3.

Using the point-slope form of a line:

y - y1 = m(x - x1) Take the point (-3, 3):

y - 3 = 3(x -(-3)

y - 3 = 3x + 9

y = 3x + 12.

Where q crosses the y-axis x = 0 so we have

y = 3(0) + 12

y = 12

The required point is (0, 12).

Answer 2

(0, 12 )

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, 3) and (x₂, y₂ ) = (- 5, - 3)

m =
`(-3-3)/(-5+3)` =
`(-6)/(-2)` = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 3, 3 ), then

3 = - 9 + c ⇒ c = 3 + 9 = 12 ← y- intercept

Thus the line crosses the y- axis at (0, 12 )