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# determine the intercept, then graph the line?

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4x + 5y + 6 = 0

Jul 28, 2017

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To determine the intercepts of this equation in the form $$ax+by+c=0$$, I would just make x and y zero and see what the result is:

Finding the x-intercept

For a line without the slope of 0, the line only touches the x-axis once. For a point to be on the x-intercept, y must be zero; otherwise, it would not be on the x-intercept. Knowing this, you can set the y to be zero and solve for x:

 $$4x+5y+6=0$$ Make y=0 so that the point is on the x-intercept. $$4x+5*0+6=0$$ $$4x+6=0$$ Subtract 6 on both sides. $$4x=-6$$ Divide by 4 on both sides. $$x=\frac{-6}{4}=-\frac{3}{2}=-1.5$$

Ok, we have determined that the x-intercept is located exactly on the point $$(-\frac{3}{2},0)$$

Finding the y-intercept

You will utilize the exact same logic to find the y-intercept. Of course, x will be equal to 0 this time:

 $$4x+5y+6=0$$ Substitute 0 in for x. $$4*0+5y+6=0$$ $$5y+6=0$$ Subtract 6 on both sides. $$5y=-6$$ Divide by 5 on both sides. $$y=-\frac{6}{5}=-1.2$$

Ok, we have determined that the y-intercept is located exactly on the point $$(0,-1.2)$$.

You actually do not need any more information to graph this equation. Plot both the intercepts on a coordinate plane, and use a ruler to connect them. Then, you are done!

Jul 28, 2017