Were given a point in a line and in part a were asked to write the equation of the line through this point. In parallel to the given line, the line is equation five X plus three y equals zero, and the point on the line is 7/8 3 4th now. As I said in part, they were looking for the wine parallel to the given line in order to do this. That's right, our line in slope intercept form So we have Y is equal to negative five X, but then divide by three. So it's negative five thirds x. From this, we see that the slope of our original line is negative five thirds, and therefore, the slope of our new line, which is parallel to the original line, is also negative. Five thirds. Now we have the slope of the new line and a point on it, so we'll use Point Slope form to write the equation of this line. So we have Y minus the y. Coordinate 3/4 over X minus. The X coordinate 7/8 equals slope negative five thirds solving for why have y minus 3/4 equals negative five thirds x plus, then we have 7/8 times five thirds is 35 24th. Solving for y y equals negative five thirds x plus 35 24th plus 3/4. This is the same as plus 18 24th, so we have 35 plus 18 is 53 24th. And so this is the equation of the line through the given point in parallel to our given line that in part B, we want to find the equation of the line through the given point and perpendicular to the given line. To do this, we want to find the slope of the given of the new line. We know the slope of the new line is going to be the negative reciprocal of the slope of the Given mine, which we found was negative five thirds. So flipping and multiplying the denominator, we get 3/5. This is the slope of our new line. We have the slope of the new line and a point on the new line, so we'll use point slope form. That's right, the equation of the new line. Yeah, so this tells us why. Minus the y coordinate 3/4 over x minus The X coordinate 7/8 equals the slope 3/5 Southern for why we have. Why minus 3/4 equals 3/5 x minus 21 40th So that why is equal to 3/5 x minus 21 40th plus 3/4 their words minus 21 40th plus 70th We're plus nine Fortius. So this is the equation of the line perpendicular to the given line in passing through the given point.