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The y-intercept is the value of y when x=0

Emma, the answers above all provide some different ways to help you understand the question you asked. You had to use both your math knowledge and critical thinking skills to arrive at the right solution. Now you should be ready to move on the new challenges!

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Emma,

The standard equation for a line is :

y = ax + b

y is called the dependent variable because its value depends on the value of x

a is the slope of the line

x is called the independent variable because it can be any value

b is the y-intercept

In your case : y(x) = 5x, y(x) is just another way of writing the equation to indicate that y is a function of x. You could simply write it as y = 5x. Thus if we compare to the standard form equation y = ax + b, a=5 and b=0. Thus the y-inercept is zero. The reason that this is the case is that when you set x=0 the value is plotted on the y axis, because the equation for the y axis is the line defined by x=0. Any value in the x,y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the y axis.

The x-intercept is a little harder to find. We have to set y=0 as that is the line defining the x axis. We start with the original equation. y = ax + b. Setting y=0 gives ax+b = 0. Subtracting b from both sides gives ax = -b. Finally dividing both sides by a yields the x-intercept, x = -b/a.

From above for y=5x, a=5 and b=0, the the x-intercept would be -0/5 which is also 0. So when b=0 the line goes through (0,0) otherwise known as the origin.

Hi Emma,

If we are given a function where the "y" value depends on the "x" value, the y-intercept (where the function crosses the y-axis) is simply the y-value when x=0, because at the y-axis, x=0.

(y, as a function of x) y(x) = 5x

y(0) = 5(0) (the function value, with "0" plugged in for the "x" value)

y(0)=0

So the y-intercept is 0. This function crosses the y-axis at a y value of 0.

Emma, think of this as being in the form y = mx + b, where m is the slope and b is the y-intercept.

Because there is no b in the equation, then b = 0. We just don't write y = 5x + 0.

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