How to find the gradient and y intercept on these questions?

3x+2y=1


3y+4x=2





I really need the theory to this as well as the answers, i think i nearly have it but this would help a lot





Thanks





GabeHow to find the gradient and y intercept on these questions?
GIVEN





3x+2y=1





and what you need to do is to convert the above in the standard slope-intercept form which is





y = mx + b





where





m = slope (or gradient) of the curve


b = y-intercept





To convert the given equation to the standard slope-intercept form, do the following steps.





Step 1 -- isolate the ';y'; term





2y = - 3x + 1








Step 2 -- divide both sides with the factor such that the numerical coefficient of ';y'; will be 1. In this case, divide both sides by ';2';





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





NOTE that the above is now in the form of the standard slope-intercept equation. Therefore,





m = slope = -3/2





and





b = y-intercept = 1/2





I will leave it up to you to solve the second problem. Simply follow the same steps as in the previous problem.





Hope this helps.





How to find the gradient and y intercept on these questions?
The y intercept is where it intercepts the y-axis. At that point x = 0, so put 0 in for x and solve for y.





3x+2y=1


3(0) + 2y = 1


0 + 2y = 1


2y = 1


y = 1/2





3y + 4x = 2


3y + 4(0) = 2


3y + 0 = 2


3y = 2


y = 2/3





For gradient, it's easier to put them in y =- mx + b form (and that also makes it easier to see the y intercept. That's why it's called the slope/gradient form. Solve the equations for y. The slope is the coefficient on x and the constant at the end is the intercept.





3x+2y=1


2y = -3x + 1


y = -3x/2 + 1/2





slope -3/2, y-intercept = 1/2 as above





3y+4x=2


3y = -4x + 2


y = -4x/3 + 234





slope -4/3, y-intercept = 1/3 as above
Gabe -





You need to start by getting the equation into the format y = mx + b.





2y = -3x + 1


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


m = slope (gradient) = -3/2


b = y-intercept = 1/2





3y+4x=2


3y = -4x + 2


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


m = slope (gradient) = -4/3


b = y-intercept = 2/3



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





slope:(-3/2)


y intercept: 1/2








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





slope:(-4/3)


y intercept: 2/3