what is the equation of the line that passes through the points (0,10) and (2,4)

Answer 1

Hi Jokkat,

In order to find the equation of the line that passes through points (0,10) and (2,4) we will need to use the slope formula and point-slope equation.

The slope formula will help you determine the slope of this equation, and the point-slope equation will help you generate the equation after you have found the slope.

The Slope Formula is: (y(2)-y(1))/(x(2)-x(1))

The points in the word problem are in the form (x,y), therefore x(1) will be the x variable in the first point and x(2) will be the x variable in the second point. The same pattern follows for the y variables. Plug the points into the formula and the calculations are -

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

(4-10)/(2-0)

-6/2

-3

The slope is -3. We will then use the point-slope equation to find the equation of the line. The point-slope equation form is: y-y(1)=m(x-x(1))

The same rules for x(1) apply here - x(1) is the x variable in the first set of points, and y(1) is the y variable in the first set of points. m is equal to the slope. In this case m=-3. Plug in the points and the slope into the equation. You could either leave it like this or isolate y to put the equation in y=mx+b form. The calculations are:

y-y(1)=m(x-x(1))

y - 10 = -3(x-0)

y - 10 = -3(x)

Answer 2

Point Slope Formula: y-Y1=m(x-X1) (X1, Y1) Fill in the X1 and the Y1 (0,10)

m = Slope Formula: y2 -y1 / x2 - x1 (x1, y1) (x2, y2) (0,10) (2,4)

m = 4-10 / 2-0

m= -6/2 = -3 Watch your signs

Now plug it all in: y-10= -3(x-0) - Distribute the -3 Distribute means to multiply -3(x) and -3(-0)=0

y-10= -3x

+10 +10 Isolate the y by moving the -10 using inverse or opposite operation

Final answer: y= -3x + 10 Notice the 10 can not be added to the -3x.

Answer 3

y=mx+b

where m= (10-4)/(0-2) = -6/2 = -3

y=-3x+b where b= y intercept. Plug in either point to solve for b

10=-3(0) + b

b = 10

y=-3x+10 is the line through the two points