Write an equation for the line through the points (3,2) and (9,6) in point-slope form y = y_0 + m(x-x_0). y = ?

Answer 1

the solution is: y=(-2/3)x + 12 where (xo,yo) is the y-intercept (0,12)

m = rise/run, the change in y divided by the corresponding change in x. y decreases by 4 (2 to 6) when x increases by 6 (3 to 9) so slope = -4/6= -2/3

slope is also generically any (x,y) compared to either given point, such as (3,2): m=(y-2)/(x-3)=-2/3

cross multiply to get 3(y-2) = -2(x-3)

3y-6 = -2x +6

3y = -2x +6+6

y = (-2/3)x +12 the y-intercept is 12, or the point (0,12); slope = 2/3

check the answer and plug in each point and see if the equation is true

try (3,2) 2=(-2/3)(3)+12 = -2+12 =2

try (9,6) 6=(-2/3)((9)+12 = -6+12=6

y=(-2/3)x + 12 is the equation through those two points

The y-intercept is the y coordinate when x=0 which is 12

The x-intercept is the x-coordinate when y=0, or solve 0=(-2/3)x+12

(2/3)x=12

2x=36

x=18

x-intercept of the line is the point (18,0)

The line in the 1st quadrant starts at the y-intercept (0,12) and goes down 2 units as it goes to the right 3 units (m=-2/3= negative "rise"/positive run) It goes down 2 to y=10 when x increases by 3 to x=3,

down 12 to y=0 from (0,12) to the right 18, to x=18 to get to the x-intercept (18,0) 12 is 2/3 of 18

Answer 2

Hello Hot!

I believe this is Geometry, not Statistics. But I can solve it:

From the point-slope equation: m = (y-y₀)/(x-x₀)

We can use the coordinates of the two points to find the slope

m = (9-3)/(6-2) = 6/4 = 3/2

Using the point (3,2) as (x₀, y₀), we will have:

y = 2 + (3/2)*(x-3)