Find the equation of the line; given the following information: Passes through (1,-4) and is parallel to y-2x+6...

Find an equation of the line that contains the point (14,-3) and is parallel to the line $5 x+7 y=35$. Write the equation in slope-intercept form.

We're finding the equation of the line that's parallel to the line. Y equals five and goes through the 50.1 tube. So if you want to visualize the line, Y equals five, it's a horizontal line and the 0.1 to right about there. So if we want a lying parallel toe Y equals five, it's going to be another horizontal line. So that's a horizontal line. At a height of two. Every horizontal line has the equation. Why equals something? So for us, this is going to be why equals two?

So we can see because the line parallel tude. Ah, lying X plus three y goes for five. So they got the same slope. So three why you chose to fire minus acts? Why he calls to file over three miners. One third acts. So the line we need to know us How the slope peak House to minors once, sir. So why my nose for you have to minors. One certain acts plus one why you kills through miners. One third acts miners. One certain last four. So why you goes to minors? One third axe. Class A level, Overstreet.

We're finding the equation of the line that is parallel to the line y equals negative for and goes through the 0.0 negative three. So let's picture the situation. First of all, the line y equals negative. Four is a horizontal line at a height of negative four, and then the other line has to go through the 0.0 negative three. And it's parallel to the other line. So if it's parallel to it, it's also a horizontal line, and that line is at a height of negative three. So our equation is why equals negative three.

In this problem, we are asked to find the equation of a line that is parallel to this equation to the line by this equations. Why? People 60 next, minus two. And what we need to remember is a parallel line has the same slope. So what we know is that the line we're looking for is going to have y equals 60. Next, it's gonna have the same slope, but we don't know the Y intercept. So what I'm going to do is write White 16 x plus b be because I don't know the Y intercept. Leaving it is a variable. Now we also know that the values that this point goes through the coordinate point of three and negative 14. So we have an X and A Y value for this new line. So what we can do a substitute those values into this equation. So we confined, be weaken, solve for B. So it was a negative. 14 people 16 times three plus b. Okay, and now weaken. Simplify. This negative 14 equals 16 times three, which is 48 plus b and we then subtract 48 from both sides. So isolate the B B equals and negative 14 minus 48. It's negative 62. So now we have a value for B. B is negative 62 so we can rewrite this equation with that value for B or, if you like, why it goes 60 next, minus 62.