Math Problem?

Question

Find the slope and the y-intercept of two lines whose equations are 2x + y = 4 and 4x + 3y = 10. Express each equation in slope intercept form. Find the point where each line intersect.

I pretty much know how to solve this. I get (1,2) as the point of intersection. The slope intercept form for the first equation is y= -2x + 4. I just get confused with the slope intercept form for the second equation. Can someone please help me find the slope intercept form for 4x + 3y =10?

Answer 1

To get the slope and y-intercept, write the equation in the form y=mx+b.

First line: y=-2x+4, so slope is m=-2, y-intercept is b=4.

Same for second line: 3y=-4x+10, so y=(-4/3)x+10/3, so slope is -4/3, y-intercept is 10/3.

To find where they intersect, set the y-values equal to each other: -2x+4=(-4/3)x+(10/3) and solve for x.

Multiply through by 3: -6x+12=-4x+10

Rearrange: 2=2x, so x=1. Plug that into either equation to get the y-coordinate of the intersection point, which is 2.

Answer 2

The slope of a line is given by:

y=mx+c

Firstly; the y intercept is obtained when x=0
So for:
2x + y = 4
we can rearrange to give y= -2x +4
and since x=0 at the intercept we get
y= -2*(0) + 4
which gives y=4 to be the point of intercept. The slope of this line is the number before the 'x' in this case -2

Similarly for the second line:

4X+3y = 10

we can rearrange to give 3y = 10 - 4x
Dividing through by 3 to get the standard equation for a line gives:

y= (10/3) -(4/3)x

Y Intercept is obtained when x=0
so y=(10/3) -(4/3)*0
which gives y=(10/3) or 3.3333

Again the slope for this line is the number before the 'x' term -4/3.



RIGHT i'm not sure do you next ask where the two lines intersect each other? if so then...

y=4-2x and y=(10/3)-(4/3)x

we set these two lines equal to each other like so:

4-2x = (10/3) - (4/3)x

we need to get everything in terms of thirds:

(12/3) -(6/3)x = (10/3) - (4/3)x

we can add or subtract and solve for x:

(2/3) = (2/3)x

therefore x = 1

since we now know that x= 1 we can substitute this value into either of the two equations we started with to give the point of intercept.

so lets just take y=4-2x
y= 4-2*(1)
y = 2
and so the point of intersection of the two lines is (x,y) = (1,2)

Answer 3

first put the equations in slope intercept form:
y = mx + b

m = slope
b = y intercept

2x + y = 4
subtract 2x from both sides:
y = -2x + 4

the slope of this line is -2 and the y intercept is 4

4x + 3y = 10
subtract 4x from both sides:
3y = -4x + 10
divide both sides by 3
y = (-4x)/3 + 10/3
y = (-4/3)x + 10/3

the slope is (-4/3) and the y intercept is 10/3

to find out where they intersect, graph them on a graphing calculator together and look at the graph to see where they intersect.

Answer 4

for the first one:
subtract 2x from both sides to get: y= -2x + 4
the slope is negative 2 and the y-intercept is 4

the second one:
subtract 4x from both sides to get: 3y= -4x + 10
then divide everything by three
that leaves you with
y= -4/3x + 3 1/3
negative 4/3 is your slope and your y-intercept is 3 and 1/3

Once you graph these, they intersect at (1,2)

Answer 5

Pick some variables that solve the equation, and then graph it on graph paper and measure slopes, read intersect off graph. They intersect at x=1 and y=2. Can also do by trial in error or by just looking at the equations and seeing the anwers in your head.

Answer 6

You need to isolate y.

So, move the 4x to the RHS of the equation

3y = -4x + 10

Now you need to divide both sides by 3 to isolate y.

y = (-4/3)x + (10/3)

There you go!

Answer 7

Solve these using simultaneous equations.

The easiest way of doing this is to set both equations to the form 3y=...

and subtract one from the other to find x. Then use this value of x in one of the equations to find y.

Answer 8

2x+y=4
y=-2x+4
m=-2
b=4

4x+3y=10
3y=-4x+10
y=(-4/3)x+10/3
m=-4/3
b=10/3

2x+y=4
4x+3y=10
multiply the 1st equation by -2
-4x-2y=-8 add to 2nd eqn
4x+3y= 10
_________
y=2

substituting in 1st eqn
2x+2=4
2x=2
x=1

the point of intersection is (1,2)