# The equation of a line is #y=mx+1#. How do you find the value of the gradient m given that #P(3,7)# lies on the line?

##### 1 Answer

#### Explanation:

The problem tells you that the equation of a given line in *slope-intercept form* is

#y = m * x + 1#

The first thing to notice here is that you can find a **second point** that lies on this line by making **intercept**.

As you know, the value of

#y = m * 0 + 1#

#y = 1#

This means that the point **slope** of the line, *change in* *change in*

#m = (Deltay)/(Deltax)#

Using

#{(Deltay = 7 - 1 = 6), (Deltax = 3 - 0 = 3) :}#

This means that the slope of the line is equal to

#m = 6/3 = 2#

The equation of the line in slope-intercept form will be

#y = 2 * x + 1#

graph{2x + 1 [-1.073, 4.402, -0.985, 1.753]}