Maria's Responses in WyzAnt Answers

The first thing we want to do is to find the slope between these two points.  The equation for the slope, m, is:

m=rise/run=(y₂-y₁)/(x₂-x₁).

Let the first point (-1,0)=(x₁,y₁) and the second point (1,2)=(x₂,y₂), then

m=(2-0)/(1-(-1))=2/2=1, so the slope between these two points is 1.

Now, we can write the equation of the line in point-slope form, where m is the slope:

y-y₁=m(x-x₁)

y-0=1(x-(-1))

y-0=1(x+1) or y=1(x+1), which is the equation of the line in point-slope form.  Note: Instead of (x₁,y₁), you could also use (x₂,y₂).  Your point-slope form equation will then look like: y-2=1(x-1), which will still give you the same equation for the slope-intercept form once you rearrange the equation.

The equation for slope-intercept form is, where m is the slope and b is the y-intercept:

y=mx+b

So we just want to rearrange our equation of the line in point-slope form so that it looks like the equation of the line in slope-intercept form.  To do that, we re-write y=1(x+1) as:

y=1x+1 where the 1 was distributed through the parenthesis.  So the equation of the line in slope-intercept form is:

y=x+1

And for this equation, we see that b=1, so the equation goes through the y-axis at y=1.

Hope that helps!

The point slope form is written like this:

y-y₁=m(x-x₁) where m is the slope, and (x₁,y₁) can be either one of the two points you are given.  First, we need to find the slope m from the given points.

The slope m=rise/run=(y₂-y₁)/(x₂-x₁). Let (2,3)=(x₁,y₁) and (5,1)=(x₂,y₂).  Then the slope is:

m=(1-3)/(5-2)=-2/3

Now put the point (2,3) in the point-slope equation along with the slope m to find the equation of the line between the two points.

y-3=(-2/3)(x-2)   Now distribute -2/3 through the parentheses, and add 3 to both sides

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

y=(-2/3)x+13/3    The term 13/3 is (4/3)+3 written in fraction form.  This is the equation of the line in a form called slope-intercept form.  In slope-intercept form, the slope is still -2/3, and the place where the line intercepts the y-axis is 13/3.

Hope that helps a bit!

The problem I believe you are trying to solve is:

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

The first step we want to take is to cross multiply.  When we do that, the result is:

4(2x-1)=3(x+2)

Now we distribute the 4 and 3 through the parentheses:

8x-4=3x+6

Next we solve the equation for x by isolating x on one side of the equation.  First I'll add 4 to both sides of the equation:

8x=3x+10

Then subtract 3x from both sides of the equation

5x=10

Now divide by 5, and you get x=2

You can double check the answer by plugging x=2 back in to the original equation. When we do, we find that both sides of the equation are equal to each other, meaning our solution is correct!

Here is a Hint:

Multiply the whole equation by t.  The result will then be:

ct=3t²+8 (subtract ct from both sides)

0=3t²-ct+8

Now apply the quadratic formula to solve for t.

Hope this answer is useful!

It is important to use parentheses when multiplying/dividing by fractions.  Do you want to solve:

(1/3)x+2/3=(5/3)x

or

1/(3x)+2/3=5/(3x)

The answer will be different depending on where the parentheses are placed.  In the first equation, the fractions are being multiplied by x, and in the second equation, x is in the denominator of the fraction.