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
Jan 9, 2017

Answer:

#m = 2#

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 #x=0#, i.e. by looking at the value of the #y#-intercept.

As you know, the value of #y# that you get for #x=0# corresponds to the #y#-intercept. In this case, the #y#-intercept is equal to #1#, since

#y = m * 0 + 1#

#y = 1#

This means that the point #(0,1)# lies on the given line. Now, the slope of the line, #m#, can be calculated by looking at the ratio between the change in #y#, #Deltay#, and the change in #x#, #Deltax#

#m = (Deltay)/(Deltax)#

Using #(0,1)# and #(3,7)# as the two points, you get that #x# goes from #0# to #3# and #y# goes from #1# to #7#, which means that you have

#{(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]}