# Thread: Help with finding y-intercept using gradient and x -intercept

1. ## Help with finding y-intercept using gradient and x -intercept

Given gradient (-2/3) y intercept (3)
Question Use the gradient to find the y coordinate on the line were
x=6
my working out
y2-y1/x2-x1
y-0/0-6 = 2/3 (Negative)
y/-6=2/3(Negative)
y=(negative) 2/3 x (negative) 6/1
y=12/3
y=4
I know the answer is supposed to be negative but I don't know where I went wrong.
Also the answer is negative 1.

2. ## Re: Help with finding y-intercept using gradient and x -intercept

Originally Posted by Ito4
Given gradient (-2/3) y intercept (3)
Question Use the gradient to find the y coordinate on the line were
x=6
my working out
y2-y1/x2-x1
y-0/0-6 = 2/3 (Negative)
y/-6=2/3(Negative)
y=(negative) 2/3 x (negative) 6/1
y=12/3
y=4
I know the answer is supposed to be negative but I don't know where I went wrong.
Also the answer is negative 1.
Doing it your way using the gradient formula.

You have the point (0, 3) ie the y intercept. And you need to find y where (6, y) is on the line.

$\frac{y-3}{6-0}=\frac{-2}{3}$
$y-3=\frac{-2}{3}*6$
$y-3=-4$
$y=-1$

Alternatively:
The equation of a straight line with gradient m and y-int c is y=mx+c.

So
the equation of the line with gradient $\frac{-2}{3}$ and y-int 3 is $y=\frac{-2}{3}x+3$

Now substitute x=6 to get y=-1

3. ## Re: Help with finding y-intercept using gradient and x -intercept

Originally Posted by Ito4
Given gradient (-2/3) y intercept (3)
Question Use the gradient to find the y coordinate on the line were
x=6
my working out
y2-y1/x2-x1
y-0/0-6 = 2/3 (Negative)
You sad "y intercept 3" but there is no "3" in this equation! You are using (0, 0). That would be with the line crossing the y-axis at the origin, not at (0, 3). Also in the numerator, your "y2" is "y" and "y1" is 0 but the denominator has "x2" equal to 0 and "x1" equal to 6. That's reversed. Your given point is (x2, y2)= (6, y) and the y intercept is (x1, y1)= (0, 3). It should be "y- 3" in the numerator and "6- 0" in the denominator:
$\frac{y- 3}{6- 0}= -\frac{2}{3}$so that $y- 3= -\frac{2}{3}(6)= -4$ and then $y= 3- 4= -1$.

y/-6=2/3(Negative)
y=(negative) 2/3 x (negative) 6/1
y=12/3
y=4
I know the answer is supposed to be negative but I don't know where I went wrong.
Also the answer is negative 1.
Why do you keep writing the word "negative"? Doesn't your key board have a "-" just to the right of "0"?