# How do you translate a graph to the left or right?

Oct 25, 2014

When translating a graph to the left or to the right, it means moving the entire graph to the left or to the right of its current location, which is usually relative to $\left(0 , 0\right)$

For example, let's say you have a circle centered at $\left(0 , 0\right)$ with radius 2. Its standard equation would be

${x}^{2} + {y}^{2} = 4$

Now, let's say we translate the circle 5 units to the left. Your circle will now be centered at (-5, 0) with the radius still equal to 2. Its new standard equation would be

${\left(x + 5\right)}^{2} + {y}^{2} = 0$

This is also true for linear equations.
For example, let's say you have a line with slope 1 with the x-intercept equal to 0. Its equation will be

$y = x$

When we translate the line 3 units to the right, its slope will remain the same, but its x-intercept will now be 3. Its new equation will be

$y = x - 5$