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

1 Answer
Stefan V.
Jan 9, 2017

m = 2m=2

Explanation:

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

y = m * x + 1y=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=0x=0, i.e. by looking at the value of the yy-intercept.

As you know, the value of yy that you get for x=0x=0 corresponds to the yy-intercept. In this case, the yy-intercept is equal to 11, since

y = m * 0 + 1y=m⋅0+1

y = 1y=1

This means that the point (0,1)(0,1) lies on the given line. Now, the slope of the line, mm, can be calculated by looking at the ratio between the change in yy, 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]}

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