Find, in slope-intercept form, the equation of a line parallel to 𝑦 equals negative eight-thirds 𝑥 plus three, that passes through point 𝐴: negative three, two.
To solve this problem, we can use the point slope formula. The point slope formula says 𝑦 minus 𝑏 equals 𝑚 times 𝑥 minus 𝑎, where 𝑚 equals the slope and 𝑎, 𝑏 is the given point.
In our problem, we’ve been given both, the point and the slope. You might be curious what the slope is since our question doesn’t explicitly say the slope. That’s okay because our question tells us that the line is parallel to 𝑦 equals negative eight-thirds 𝑥 plus three. And we know that parallel lines have the same slope. The slope of the line 𝑦 equals negative eight-thirds 𝑥 plus three is negative eight-thirds. And since parallel lines have the same slope, the slope of our line is also negative eight-thirds.
We have a slope. Now we also have a point, negative three, two. Let’s plug everything in. Plug in two for 𝑏, so 𝑦 minus two equals negative eight-thirds, plugged in for 𝑚, times 𝑥 minus negative three. Negative three, it’s been plugged in for 𝑎.
Now we can simplify this equation. We’ll say that 𝑥 minus negative three equals 𝑥 plus three. Then we need to distribute our negative eight-thirds, to 𝑥 and three. Negative eight-thirds times 𝑥 equals negative eight-thirds 𝑥. Negative eight-thirds times three equals negative eight.
We’re nearly there with our slope intercept form. But for slope intercept form, we need 𝑦 by itself. To do that, we add two to both sides of our equation. On the left, we’re left with 𝑦 and on the right, negative eight-thirds 𝑥 minus six.
The equation of a line parallel to 𝑦 equals negative eight-thirds 𝑥 plus three — that also passes through point negative three, two — equals negative eight-thirds 𝑥 minus six.