how do i find the equation of a line through the points (3,1) and (5,2).?

Question

please help i dont understand!

Answer 1

first slope, change in y (dy) over change in x (dx). dy = 2-1 = 1. dx = 5-3 = 2. so slope = 1/2

equation is y = 1/2 x + b, where b is y-intercept. to find b, plug in one of the points:

2 = (1/2)(5) + b
2 = 5/2 + b
-1/2 = b.

y = (1/2)x - 1/2

Answer 2

Here is the general method.

Given: two points: (X_1,Y_1), (X_2,Y_2)

1. Find the slope. The slope, m, is given by:
m = (Y_1 - Y_2)/(X_1 - X_2). Simplify this.

2. Use Point-slope form, that is, we have:
y - Y_1 = m(x - X_1)
You can use either (X_1, Y_1) or (X_2, Y_2) but both will give the same end result.

3. Solve for y and put it in the slope intercept form of y = mx + b. In general, that is:

y = mx + (Y_1-mX_1)


Let's try this with your two points:

1. Find the slope: m = (1-2)/(3-5) = 1/(-2) = -1/2.
2. Point-slope form: y - 1 = -1/2(x - 3)
3. Slope-intercept:
y = -1/2 + 3/2 + 1
y = -1/2 + 5/2

Answer 3

slope intercept form