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EastWind [94]
3 years ago
6

Write an equation of the line passing through (-3,4) and (6,5) and give the answer in standard form

Mathematics
1 answer:
Andru [333]3 years ago
3 0
Let's start by putting it into slope-intercept form, which is
y=mx+b where m=slope and b=y-intercept (the value of y when x=0)

Find the slope between (-3, 4) and (6, 5).
Formula for slope: m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}
Plug in our x and y values...
m=\frac{5-4}{6-(-3)}=\frac{1}9
Our slope is 1/9.

We can interpret this slope rise/run = 1/9 as
<em>"When y changes by 1, x changes by 9. (and vice versa)"
</em>We want to find the y-intercept. (the value of y when x=0)
Let's take the point (-3, 4).
We want to add 3 to that x to make it 0.
According to our slope, this means adding 1/3 to y. (1 to 9 = 1/3 to 3)
Our y-intercept is at (0, 4 1/3), with the value we use in our eqn. b = 4 1/3.
Let's use an improper fraction, b = 13/3.

Now our equation is y=\frac{1}9x+\frac{13}3
Let's convert to standard form, ax+by+c=0.
Just multiply by the LCD of our fractions (in this case, 9)
9y=x+39
Now move everything to the left side.
\boxed{-x+9y-39=0}
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Answer:

p^2 + q^2 = 22/9.

Step-by-step explanation:

For a quadratic function ax^2 + bx + c if the zeroes are A and B then

A + B = -b/a and AB =  c/a.

2x^2 - 7x + 3

Now p and q are the zeroes of the above function so

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Now p^2 + q^2 = (p + q)^2 - 2pq

= (7/3)^2 - 2* 3/2

=  49/9 - 3

= 49/4 -  27/9

= 22/9.

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Answer:

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