Find, in slope intercept form, the equation of the line perpendicular to 𝑦 equals two 𝑥 minus four that passes through the point 𝐴: three, negative three.
To solve this problem, we’ll use the point slope formula which says: 𝑦 minus 𝑏 equals 𝑚 times 𝑥 minus 𝑎, where 𝑚 equals the slope and 𝑎, 𝑏 equals the given point. To start, we’ll need to figure out what the slope of our line is. We weren’t told the slope. But we were told that our line is perpendicular to 𝑦 equals two 𝑥 minus four.
Here’s what we know about perpendicular lines and their slopes. Perpendicular lines have negative reciprocal slopes. The slope of the line we’re given is two. And the negative reciprocal of two equals negative one-half. Our 𝑚-value is negative one-half. And our given point is three, negative three. So let’s plug in what we know.
We can plug in negative three for 𝑏-value. Our slope equals negative one-half. And our 𝑎-value equals three. Now let’s take this information and simplify it to put it in slope intercept form. We could change 𝑦 minus negative three to 𝑦 plus three. We distribute the negative one-half to both the 𝑥 and to the negative three which gives us negative one-half 𝑥 plus three over two.
Because slope intercept form is in the format “𝑦 equals”, we’ll need to isolate 𝑦. So we subtract three from both sides of our equation. When we subtract three from three over two, we’re left with negative three-halves.
So we say that, in slope intercept form, our equation: 𝑦 equals negative one-half 𝑥 minus three-halves.