Question

Given: AB and CD

If the coordinates of point A are (8, 0) and the coordinates of point B are (3, 7), the y-intercept of AB is ________. If the coordinates of point D are (5, 5), the equation of line CD is y = _____
x + _____.

Answer 1

@AdoNine @Michele_Laino

Answer 2

here we have to write the equation of the line which passes at points A and B, first

Answer 3

Okay

Answer 4

the slope \(m\) of such line, is given by the subsequent computation:
\[m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{7 - 0}}{{3 - 8}} = ...?\]

Answer 5

please complete

Answer 6

7/5?

Answer 7

hint:
\(3-8=-5\)

Answer 8

7/-5?

Answer 9

correct!

Answer 10

so thats the first part?

Answer 11

the requested equation, is:
\[\begin{gathered}
y - {y_2} = m\left( {x - {x_2}} \right) \hfill \\
\hfill \\
y - 0 = \frac{{ - 7}}{5}\left( {x - 8} \right) \hfill \\
\end{gathered} \]
please simplify

Answer 12

y=-7/5x+56/5 is correct ?

Answer 13

correct!
Next the requested \(y-\)intercept, is the value of \(y\), when \(x=0\), so we have:
\[y = \frac{{ - 7}}{5} \cdot 0 + \frac{{56}}{5} = ...?\]

Answer 14

y=56/5 ?

Answer 15

correct!

Answer 16

for second part, I think that coordinates of point C are missing

Answer 17

So for the last question I would put y=56/5x+...?

Answer 18

we need to know the coordinates of point C

Answer 19

Or what would you put after x+ ?

Answer 20

On the question it does not have any coordinates for c.

Answer 21

how point C is defined?

Answer 22

https://snag.gy/Spjkzf.jpg

Answer 23

line CD is parallel to line AB, namely, the symbol:
\[AB \parallel CD\] means line AB is parallel with respect to line CD

Answer 24

now, parallel lines have the same slope, so the slope of line CD is \(m=-7/5\)

Answer 25

the requested equation, is therefore:
\[y - 5 = \frac{{ - 7}}{5}\left( {x - 5} \right)\]
please simplify

Answer 26

hint:
if we apply the distributive property, we get:
\[y - 5 = \frac{{ - 7x}}{5} + 7\]

Answer 27

And when I simp. that what I plug into the last part?

Answer 28

y=-7/5x+12?

Answer 29

yes! Please we have this step:
I add \(5\) to both sides, so I get:
\[y - 5 + 5 = \frac{{ - 7x}}{5} + 7 + 5\]
please simplify

Answer 30

correct!