What is the equation of the line that has a slope of -2 and passes through the point (-5,0) ?

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Answer 1 · 2018-05-07T15:33:36

#color(blue)(y=-2x-10)#

If we have two points on a line:

#(x_1,y_1) and (x_2,y_2)#

Then we can say that the gradient of the line is:

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

Let #m="the gradient"#

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

And:

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

This is known as the point slope form of a line.

We know #m=-2# and we have a point #(-5,0)#

Substituting these into the slope point form, with #x_1=-5# and #y_1=0#

#y-0=-2(x-(-5))#

#y=-2x-10#

This is the required equation.