3x+2y=10 need to solve for y to determine the slope and y intercept?

Question

I have the hardest time solving to get y singled out on one side.

Answer 1

3x + 2y = 10

transpose 3x

2y = 10 - 3X
divide both side with 2 to eliminate the coefficient of y which is 2

y= 5 -3/2x

y=-3/2X + 5

m=-3/2

Answer 2

The given equation is
3x + 2y = 10
or, 3x - 3x + 2y = 10 - 3x [ subtracting -3x from both sides ]
or, 2y = 10 - 3x
or, y = 5 - (3/2)x [ divide both sides by 2 ]
or, y = - (3/2)x + 5

The slope of the straight line is the co-efficient of x, which is -3/2.
therefore, slope,m = -3/2 = -1.5

The y intercept is the constant term of the final equation, which is 5. Just think of it this way, when the line cuts the y axis, the value of x will be 0. Put x = 0 in the equation, and you will get y = 5.
So the y intercept is = 5.

Answer 3

The slope-intercept form:
y=mx+b

Subtract 3x from both sides:
2y=-3x+10

Divide 2 from both sides:
y=-3/2x+5

y=-3/2(0)+5
y=5

The slope is -3/2 and the y-intercept is 5.

Answer 4

3x+2y=10

2y=-3x+10

y=-3/2 x+5

since the standard form of the equation of a line is y=mx+b,
whereas m is the slope and b is the y-intercept,
therefore slope(m)=-3/2 and y-intercept(b)=5

Answer 5

3x+2y=10
take the x to the other side by -3x from each side
2y=10-3x
divide by 2
y=5-1.5x

Answer 6

3x + 2y = 10
2y = -3x + 10
y = -3/2x + 5

This is now of the form y = mx + c, where m is the gradient and c is the y intercept.

Slope (gradient) = -3/2
Y intercept = (0,5)

Answer 7

Well, the two options a and b provide you with enough information to figure out the slope of your equations. First step to solve these problems is to isolate your y's so that you have an equation in the form y=mx + b where m is the slope and b is the y-intercept. So for a, y= (- 16 - 3x) / 4 or simplified, y= - 4 - 3/4(x) and you can rearrange this so the equation reads y= - 3/4(x) - 4. Since the equation of the line that passes through J(5,5) is parallel to the line y= -3/4(x) - 4, it has the same slope. So your skeleton equation would read y= -3/4x + b. Now we have to solve for b and this is done by plugging in the point given, (5,5) into your skeleton equation. So, 5 = -3/4 (5) +b or simplified, 5= -15/4 +b. Add 15/4 to both sides.. 5 = -15/4 + b, 5 can be re-written as 20/4, so it would be 35/4 = b. So for part a, the equation should be y= -3/4x + 35/4. For part b, the line is perpendicular to the line 5x +2y=10 or y= (10 - 5x ) 2 or y=5 - 5/2(x) or y= - 5/2x) + 5. Since the line passing through (5,5) is perpendicular to the equation in part b, the slope for the unknown line is the reciprocal of the line in part b. It is also the opposite sign of the slope given in part b. So the skeleton equation would read, y= 2/5 x + b. To solve for b, plug in your point (5,5) and you get 5=2/5 (5) + b or 5=2 +b. Subtract 2 from both sides to isolate your b and you get 3 = b. So the equation for part b should read y = 2/5 x +3. Hope these are right :D Good luck and I hope you understood my steps.

Answer 8

y=0, x=10/3.
x=0, y=5
slope= -(5/10)3
=-3/2

Answer 9

3x + 2y = 10

3x + 2y - 3x = - 3x + 10

2y = - 3x + 10

2y/2 = - 3/2x + 10/2

y = 3/2x + 5

Slope

M = 3/2

- - - - - - - - - - -s-

Answer 10

2y = -3x + 10
y = -1.5x + 5

So the slope is -1.5, with every point y increases the x decrease 1.5. (60 degrees)