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

##### 1 Answer
Feb 16, 2016

${y}_{\text{ intercept}} = 5$
The gradient is +2

#### Explanation:

$\textcolor{b l u e}{\text{Gradient or slope}}$

The slope is the coefficient of $x$. So given that $y = 2 x + 5$
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 $\left(- 2\right) x$ then the slope (gradient) would be downwards as you move left to right.

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$\textcolor{b l u e}{\text{The y-intercept}}$

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

$y = 2 x + 5 \text{ "->" } y = 2 \left(0\right) + 5$

${y}_{\text{ intercept}} = 5$

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

$y = a x + k$

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