How do you graph #y-(-3)=-1/2(x-(0))#?

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Answer 1 · 2017-10-26T11:56:47

See a solution process below:

First, clean up the signs and parenthesis in the equation to simplify it. Remember, minus a minus is a plus;

#y + 3 = -1/2(x - 0)#

#y + 3 = -1/2x#

#y + 3 - color(red)(3) = -1/2x - color(red)(3)#

#y + 0 = -1/2x - 3#

#y = -1/2x - 3#

Next, solve for two points which solve the equation and plot these points:

First Point: For #x = 0#

#y = (-1/2 * 0) - 3#

#y = 0 - 3#

#y = -3# or #(0, -3)#

Second Point: For #x = 2#

#y = (-1/2 * 2) - 3#

#y = -1 - 3#

#y = -4# or #(2, -4)#

We can next plot the two points on the coordinate plane:

graph{(x^2+(y+3)^2-0.075)((x-2)^2+(y+4)^2-0.075)=0 [-15, 15, -7.5, 7.5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(y + (1/2)x+3)(x^2+(y+3)^2-0.075)((x-2)^2+(y+4)^2-0.075)=0 [-15, 15, -7.5, 7.5]}