find the y intercept

Question

A line has a gradient of 3 and passes through (-3,3). What is its y intercept? a)0  b)3  c)6  d)9  e)12

Answer 1

Hi, Rebecca.

You can find this on a graph by starting at (-3, 3) and counting up 3, right 1 until you get to the y-axis. (The gradient or slope is the "rise over run.") 

You can also find it by using the slope-intercept equation:  y = mx + b

Use (-3, 3) for x and y, 3 for m (the slope or gradient), then solve for b, which is the y-intercept.

3 = 3(-3) + b

3 = -9 + b

12 = b

Hope this helps!

Answer 2

Equation of a line: y = mx + b
m = slope ("gradient")
b = y-intercept

You know a pair of values for x and y, so plug them and the slope into the equation and solve for b:

Point (x, y) = (-3, 3)
m = 3

y =    mx    + b
3 = (3)(-3) + b     y=3, m=3, x=-3

3 = -9 + b

3+9 = -9+9+b    add 9 to both sides

12 = b

or b = 12

b is the y-intercept.

Answer 3

The y intercept is 12