slope-intercept?

Question

I know how to find the slope- intercept when the equation is written like this 2x + 3y = 6


But how do I find the slope intercept for the equation

2x = 1/2y + 2



The book says, "write each pair of lines in slope-intercept form. Then identify whether the lines intersect in exactly one point or if the lines are parallel or coinciding"

The second equation I know how to solve 4x - y = 13

Answer 1

Just multiply both sides of the equation 2x = 1/2y + 2 by 2. Then manipulate it into this form: y = mx + b. For the slope intercept form of the equation to be valid, the constant in front of the y term must be 1. When you do that, you get:

4x = y + 4
4x - 4 = y.

We can reflect the last equation about the equal sign to obtain:

y = 4x - 4

slope = m = 4
y-intercept = b = -4.

If we let x = 0, then y = 4(0) - 4 = 0 - 4 = -4, which confirms the y-intercept is correct. This produces the ordered pair (0, -4).

If we let y = 0, then 0 = 4x - 4 ----> 4 = 4x ----> 1 = x, which is the x-intercept of the equation. This produces the ordered pair (1, 0).

We can then plug the ordered pairs (0, -4) and ( 1, 0) into the equation for the slope of a line and see if we get 4 for an answer.

slope = m = [0 - (-4)] / (1 - 0) = 4 / 1 = 4.

So, our answer appears to be correct.

For lines which are parallel, their slopes will be equal. Check the equations to see if they have the same slope, but different y-intercepts. If they do, they are parallel.

In lines which coincide, their equations are simply multiples of each other. Look to see whether these equations are rational multiples of each other, i.e. can we multiply one of the equations by a rational number to get the other. If they aren't, they don't coincide.

If the lines intersect in only one point, then their slopes will be different. We can see that equations 1 and 2 have differing slopes. Check 1 and 3 and 2 and 3. If their slopes are all different, then you can equate each equation in turn with the others and solve for a point of intersection.

Answer 2

When you have an equation in the form of y = mx + b, then m is the slope and b is the y-intercept. This form is called slope-intercept form.

So here we have:
2x = (1/2)y + 2
2x - 2 = (1/2)y (subtract 2 from both sides)
(1/2)y = 2x - 2 (switch sides to get y on the left)
y = 4x - 4 (multiply both sides by 2)
So the slope is 4 and the y-intercept is 4.

For 4x - y = 13, use the same idea:
-y = -4x + 13 (subtract 4x from both sides)
y = 4x - 13 (multiply both sides by -1)

Two lines are either parallel (in which case the two equations have no common solutions), intersecting (in which case the two equations share one solution), or lie right on top of each other (in which case you get infinitely many solutions).

Answer 3

Slope-intercept is in the form y=mx+b so all you have to do is solve for y
If you can do those two equations, the one you're asking about is no different except that it has a fraction

We need to get y by itself
Subtract 2 from the right and from the left
2x - 2 = 1/2y
To get rid of the 1/2, we multiply both sides by the reciprocol (in this case, 2/1 or 2)
2(2x-2)=y
Distribute
4x-4=y
Rearrange
y=4x-4
Slope-intercept (Slope = 4) (y-intercept = -4)

Answer 4

the generic form for slope intercept is

y = mx + b where m is the slope
so, try to manipulate the equation so that you isolate the y value

2x + 3y = 6
add -2x to both sides
3y = -2x + 6
now divide everything by 3
y = (-2/3)x + 2

slope is -2/3 and y-intercept is 3

Given 2x = 1/2 y + 2 subtract 2 from both sides, so
2x - 2 = 1/2 y
now multiply both sides by 2
4x - 4 = y or
y = 4x - 4

slope is 4 and y-intercept is -4

4x - y = 13
add -4x to both sides
-y = -4x + 13
change all the signs (which is multiplying every term by -1)
y = 4x - 13
slope is 4 and y-intercept is -13

Answer 5

subtract 2 from both sides
1/2y = 2x - 2
multiply by 2
y = 4x - 4

Answer 6

Subtract two from both sides, then multiply by 2.

2x-2=1/2y
x-4=y