Question

The line passes through points (4,7) and (-5,-5), where the line intersects the y axis, what is the slope?

Answer 1

The two-point form of a line passing through the points (x1 , y1 ) and ( x2 , y2 ) is given by:

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

In this case:

x1 = 4 , y1 = 7

x2 = - 5 , y2 = - 5


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

y - 7 = [ ( - 5 - 7 ) / ( - 5 - 4 ) ] * ( x - 4 )

y - 7 = ( - 12 / - 9 ) * ( x - 4 )

y - 7 = ( - 3 * 4 / - 3 * 3 ) * ( x - 4 )

y - 7 = ( 4 / 3 ) * ( x - 4 )

y - 7 = 4 * ( x - 4 ) / 3

y - 7 = ( 4 * x - 4 * 4 ) / 3

y - 7 = ( 4 x - 16 ) / 3

y - 7 = ( 4 / 3 ) x - 16 / 3 Add 7 to both sides

y - 7 + 7 = ( 4 / 3 ) x - 16 / 3 + 7

y = ( 4 / 3 ) x - 16 / 3 + 21 / 3

y = ( 4 / 3 ) x + 5 / 3

This is the slope-intercept form.

slope and = 4 / 3

y-intercept = 5 / 3