+2440 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!
