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

1 Answer
Feb 16, 2016

Answer:

#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.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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