How Do I write a equation of the secant line between the points (-3,0) and (-1,-4)?

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Answer 1 · 2018-02-01T20:08:38

#y=-2x-6#

The line passes through points #(-1,-4) , (-3,0)#.

The gradient of the line is given by:

#(y_2-y_1)/(x_2-x_1)#

#:.#

#(0-(-4))/(-3-(-1))=4/-2=-2#

We can find the equation of a line if we know the gradient and a point that the line passes through. This is known as the point slope form of a line.

#(y_2-y_1)=m(x_2-x_1)#

Where #m# is the gradient.

So:

#y-0=-2(x-(-3))#

#y=-2x-6#

GRAPH:

enter image source here

Answer 2 · 2018-02-02T01:48:22

Equation of the line is #color(blue)(y + 2x = -6)#

Given two points on a line, we can write the equation of the line using the standard format

#(y - y1) / (y2 - y1) = (x - x1) / (x2-x1)#

Point A1 (-3,0), Point A2 (-1,-4)

#(y - 0) / (-4-0) = (x-(-3)) / (-1 - (-3))#

#(y / -4) = (x + 3)/ 2#

#2y = -4x - 12#

#y + 2x = -6#

graph{-2x-6 [-10, 10, -5, 5]}