write a linear equation given the following data m=3/2 b=4

Question

write a linear equation given the following data:

a)  m=3/2  b=4

b) (3, -4) (0,4)

c) m=2 (-2.5, 4)

Any and all help would be greatly appreciated.  :)

Answer 1

Using slope-intercept form  y=mx+b to solve a and b  (m is slope, b is the y-axis intercept)

a) m=3/2, b=4,

plug in:  y = (3/2)x + 4

b) first solve the slope m

 m=(y₂-y₁)/(x₂-x₁),  two poits (3,-4) (0,4) , you get the slope: (4-(-4))/(0-3)=-8/3

b is the y-axis intercept. So b is the y number when x=0, from point(0,4), we know b=4

solve the equation: y=(-8/3)x+4

 

using the point slope form  of the equation of a straight line: y-y₁=m(x-x₁) to slove c

c) point (-2.5, 4)   slope m=2  

plug in: y-4= 2 (x-(-2.5))

y-4=2x+5

y=2x+9

Answer 2

a) Here you have received a slope m = 3/2 and an intercept b = 4 where the line hits the y axis.

So with this information you should choose to use the slope intercept formula (y = mx + b )to find the equation of the line.

if you plug in the coreesponding values you will get the equation y = (3/2)x + 4.

b) You have two points given.

So using the the 2 point slope formula y - y1 = [(y2 - y1)/(x2 - x1)](x - x1) is best. Your 2 points P1 and P2 have the form: P1 = (x1, y1) = (3, -4) and P2 = (x1, y1) = (0, 4). So now you plug in all the corresponding values:

y - (-4) = [(4 - (-4))/(0 - 3)](x - 3) next simplify

y + 4 = (-8/3)(x - 3) distribute the -8/3 and you will see immediately the 3 's cancel out so you have

y + 4 = (-8/3)x  + 8 Last substract 4 from both sides of the equation

y  = (-8/3)x + 4 Tada! this is the equation of your line.

 

c) For this one you are given a point P1 = (x1, y1) = (-2.5, 4) and a slope m = 2.

So using the point slope formula y - y1 = m(x - x1) is best.

So plug in: y - 4 = 2(x - (-2.5))

Now simplify: y - 4 = 2x  + 5

And solve: y = 2x + 5 + 4 which is the same as y = 2x + 9 Tada! there is your answer.

 

Hope I helped :)