which is an equation of the line with slope 2/3 that passes thru the point (4, -1)?

Question

a) y = -1/4 x + 2/3
b) y = -4x + 2/3
c) y = 2/3x - 5/3
d) y = 2/3x - 11/3

also tell me how u got the answer step by step

Answer 1

an equation for a straight line is y=mx + c, where m is the gradient/slope and c is the y intercept.

so

y = 2/3x + c

to find c you simply put the value of the point (4, -1) into the equation:

-1 = 2/3*4 + c
-1 = 8/3 +c
-1 - 8/3 = c
-11/3 = c

therefore, when you put it together

y = 2/3x - 11/3

(answer d)

Answer 2

If one has to choose from the four alternatives given, let us concentrate on alternatives c) and d) ,for, in both the cases, the slope is 2/3. Now test whether the point (4, -1) passes through y = 2/3x - 5/3. if x=4 is put in this equation, y becomes 1; not -1. So (4, -1) does not lie on this. The other alternative is y = 2/3x - 11/3. If x = 4 here, y becomes - 1. This is therefore the correct answer, i.e. d)

To outright solve the problem, we can assume any st. line y = 2/3x +a is having slope 2/3. Now if it passes through (4, -1) then -1= 2/3(4)x +a must be true. This yields a =- 11/3.

Still in another way, y - (-1) = m(x -4) is the equation of any st. line passing through (4, -1) . Simply put m = 2/3 as per the question and simplify. Almost we have nothing to work out!

Answer 3

basically keep in suggestions the easy formula for looking the slope: y2-y1 _____ x2-x1 you've already got the criteria, so basically plug them in. Then when you've your slope (the m in y=mx +b) pig a pair of issues (both pair will suffice.) case in point, utilising aspect (2,3) the equation would seem as if this: 3=m(i.e. the slope that you discovered) * 2 + b Then basically make certain for b and plug on your solutions. Does that help? i'm no longer particular the thanks to furnish the point-slope equation, yet i'm particular you'll discover the formula on line. solid success.

Answer 4

D.) B/C your have your slope and your point.
Plug in the x and y values. And solve to find b.
-1=(2/3)(4)+b
-1=(8/3)+b suntract (8/3) from both sides
(-11/3)=b plug in your answer to original equation
y=(2/3)x-(11/3)

Answer 5

m = 2/3 is gradient
passes thro` (4 , - 1)

y - b = m(x - a)

y - (-1) = (2/3)(x - 4)

y + 1 = (2/3)x - 8/3

y = (2/3)x - 8/3 - 1

y = (2/3)x - 11/3 which is answer d)

Answer 6

option (d) formula is/
y-y1=slope(x-x1)
where (x1,y1) is the point (4,-1) substituting this in the above equation u get, (y+1)=2/3(x-4)
therefore 2x-3y=11
so 3y =2x-11
y=2/3x -11/3

Answer 7

eqn of line is of the form

y = mx + c

where m is the slope

thus either c or d can only be the ans


now since it passes thru 4 , -1 substitute & check


d is correct ans