Confused mom thanks for your help.

Question

Find the X and Y intercepts of the line that passes through the given points (-6,4), (3,-5)

Answer 1

slope = m = [ -5 - 4 ] / [ 3 - -6]
= -9/9
= -1
so
y = -x + b
4 = 6 + b
so
b = -2
so equation is
y = -x -2

x axis intercept when y = 0
so (-2,0)
y axis intercept when x = 0
so (0, -2)

Answer 2

In this case :

x1 = - 6 , y1 = 4

x2 = 3 , y2 = - 5

Equation of a straight line from 2 points :

y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] ( x - x1 )

y = 4 + [ ( - 5 - 4 ) / ( 3 - ( - 6 ) ) ] ( x - ( - 6 ) )

y = 4 + [ ( - 9 ) / ( 3 + 6 ] ( x + 6)

y = 4 + [ ( - 9 ) / 9 ] ( x + 6)

y = 4 + ( - 1 ) ( x + 6)

y = 4 + [ - 1 * x + ( - 1 ) * 6 ]

y = 4 - x - 6

y = - x - 2

x - intercept is a point on the graph where y = 0

y - intercept is a point on the graph where x = 0

So :

x - intercept

y = - x - 2 = 0

- x - 2 = 0 Add 2 to both sides

- x - 2 + 2 = 0 + 2

- x = 2 Multiply both sides by - 1

x = - 2

Coordinates of x - intercept :

x = - 2 , y = 0

OR

( - 2 , 0 )

y - intercept

y = - x - 2

x = 0

y = - ( 0 ) - 2 = 0 - 2 = - 2

Coordinates of y - intercept :

x = 0 , y = - 2

OR

( 0 , - 2 )