equation slope intercept

Question

Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form.

Answer 1

Hi Yittel,

Thanks for your question! To get the equation of a line, we first need to get the slope between the points (1,1) and (2,4). Recall that slope is determined by the formula

1. m = (y2 - y1)/(x2 - x1) for a pair of points (x1,y1) and (x2,y2).

Therefore, the slope of our line is

1. m = (4-1)/(2-1) = 3/1 = 3.

Once we know the slope of our line and at least one point on the line (it can be any point on the line), we can write the equation of the line in point-slope form:

1. y - y0 = m*(x - x0), where m is the slope and (x0,y0) is a point on the line.

In our case, m = 3 and (x0,y0) can be either (1,1) or (2,4). (It makes no difference in the final answer.) For simplicity, let's choose (x0,y0) = (1,1). Then, the equation of our line in point-slope form is

1. y - 1 = 3*(x - 1).

We can write this in slope-intercept form as

1. y = 3x - 2,

which is our final answer.

Answer 2

y = m x + b

If the line goes through (1 ; 1), then

1 = m + b

If the line goes through (2 ; 4), then

4 = 2 m + b

Subtracting the first equation from the second gives

m = 3

Substituting m = 3 into the first equation gives

1 = 3 + b, and solving for b we get b = 1 - 3 = - 2

Hence the resulting equation is

y = 3 x - 2