9 - 15y 10x Find the slope and the y intercept?

Answer 1

I'll assume your question is:

9 - 15y = 10x, since we need an equation to figure out the y-intercept and slope.

To put it simply, the slope is how tilted a line is. You can think of it as the "steepness" of the line if you were walking along it from left to right.

The y-intercept is also simple, that is the point where the graph of your line touches the Y-axis (the up and down one)

In order to figure these 2 pieces out, let's rearrange your line formula into "standard form".

it should look like : y = (slope)* X + y intercept OR y = mx +b. b can be negative as well (-b), but generally we say +b.

m = slope

b = y-intercept

So we need y by itself on the left.

9 - 15y = 10x (I'm going to subtract 9 from both sides)

-15y = 10x -9 (Remember to pay attention to your positive and negative signs)

y = (-10/15) X + (9/15) (now divide everything by -15)

or, if we simplify as much as we can

y = (-2/3) X + (3/5)

You have your answer :D

Just look at the number in front of X --- (-2/3) [ negative two thirds ], this is your slope.

the number that comes after X (in standard form!!!) is your Y-intercept -- (3/5) [ three fifths]

To graph this line, y = (-2/3) X + (3/5), start at the origin and go UP three-fifths (fraction y-intercepts are not nice, but you can approximate) and put a dot on the Y-axis.

Now, our slope tells us how tilted our line is going to be. Since (-2/3) is negative, we know our line is going to go "downhill", from left to right, starting at the y-intercept.

Remember, slope is up/down first (the top number of your fraction), then left/right (the bottom number of your fraction).

Starting at our dot on the y-axis, move 2 spaces down (because -2 means go down 2 spaces) -- don't make a dot yet! -- and then move 3 spaces to the right (because 3 means right 3 spaces. if it were -3 we would go left). Now make a dot.

You can continue moving down 2, right 3 spaces until you run out of graph paper.

Or you can go back to your starting point (y-intercept) and do the opposite. Move up 2 spaces, and left 3 spaces and then make a dot. Again, continue until you run out of room.

You'll know you've graphed the line correctly if you can connect the dots with a ruler and all of the points you made are on the same straight line.

y = mx + b, the standard form of your equation is called a LINEAR equation. (see the word "line" in LINEar?)

There are other types of lines you'll learn about later, too!

For extra practice, try to find the Y-intercept and slope of these formulas:

1) y = (3/5) X - 5

2) 4y + 4 = 16X

Remember, if it doesn't look like Y = mX +b (m = slope, b = y-intercept), use your algebra to rearrange the equation until it does (hint: practice #2). If it already looks like y= mx+b (hint... practice problem #1) don't do anything to it! Circle the "m" part, this is your slope! Circle the "b" part, this is your y-intercept!... and you're done, no work needed! :D

Good luck!