Question

How do you find the slope and y intercept of `y=2x+5`?

Answer 1

`y_(" intercept")=5`
The gradient is +2

Explanation:

`color(blue)("Gradient or slope")`

The slope is the coefficient of `x`. So given that `y=2x+5`
the gradient (slope) is 2.

This means that for every 1 along the axis (left to right) the y-value increases by 2. This means that there is an upwards slope for left to right (standard direction).

If the slope had been negative; that is `(-2)x` then the slope (gradient) would be downwards as you move left to right.

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`color(blue)("The y-intercept")`

The y-intercept occurs when `x=0` so substitute this value into the original equation and solve for y

`y=2x+5" "->" "y=2(0)+5`

`y_(" intercept")=5`

In other words; it is the constant where if the constant is k and the coefficient of x is a then we have:

`y=ax+k`

So in this case the y-intercept is the value of k