# Thread: Help with finding the x and y intercepts using the gradient

1. ## Help with finding the x and y intercepts using the gradient

Given a gradient (3) and a x intercept (-3) supposed to find the y intercept.
My working out
Y/X = M
Y/-3 =3
Y/-3 X -3 = 3 x -3
Y=-9
But the book says it's 9, and I don't know why?

2. ## Re: Help with finding the x and y intercepts using the gradient

The line crosses the x-axis at (-3, 0) and goes upward because it has positive slope- how could it possibly have negative y intercept?

Your very first equation is wrong: Y/X= M is incorrect because that only applies when the graph passes through (0, 0). What is true is that $\displaystyle \frac{\Delta y}{\Delta x}= M$ or $\displaystyle \frac{y_2- y_1}{x_2- x_1}= M$ where $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ are two points on the line and $\displaystyle \Delta y= y_2- y_1$ and $\displaystyle \Delta x= x_2- x_1$. Here one point is (-3, 0) (the x-intercept) and another is (0, y) (the unknown y- intercept). You should have $\displaystyle \frac{y- 0}{0- (-3)}= 3$.

3. ## Re: Help with finding the x and y intercepts using the gradient

Thanks for answering but my question is how do you know it's going upward.

4. ## Re: Help with finding the x and y intercepts using the gradient

No, these questions don't sound stupid- they sound like you are memorizing formulas without understanding what they mean! I know the line is going upward because that is what "slope" means! The slope measures the rate at which the y-value is increasing relative to the x-value. Positive slope means y is increasing, negative slope means y is decreasing.

"for the very last equation y can't equal 9 because the answer will be 3."

What answer? The answer to what question? The last equation is $\displaystyle \frac{y}{3}= 3$. y has to be 9 to satisfy that.