mbehrenourts
Answered

a line passes through (3, –2) and (6, 2). a. write an equation for the line in point-slope form. b. rewrite the equation in standard form using integers. a. y minus 2 equals four thirds times the quantity x minus 3 end of quantity; negative 4 x plus 3 y equals 18. b. y plus 2 equals four thirds times the quantity x plus 3 end of quantity; negative 4 x plus 3 y equals negative eighteen. c. y minus 3 equals four thirds times the quantity x plus 2 end of quantity; negative 4 x plus 3 y equals 17. d. y plus 2 equals four thirds times the quantity x minus 3 end of quantity; negative 4 x plus 3 y equals negative eighteen.

Verified Answer :

nobillionaireNobley

\(\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \frac{y-(-2)}{x-3} = \frac{2-(-2)}{6-3} \\ \frac{y+2}{x-3} = \frac{2+2}{6-3} \\ \frac{y+2}{x-3} = \frac{4}{3} \\ y+2= \frac{4}{3} (x-3)\)
In standard form
\(y+2= \frac{4}{3} (x-3) \\ 3(y+2)=4(x-3) \\ 3y+6=4x-12 \\ -4x+3y=-18\)

calculista

Answer:

Part A) \(y+2=\frac{4}{3}(x-3)\) ----> y plus \(2\) equals four thirds times the quantity x minus \(3\) end of quantity

Part B)  \(-4x+3y=-18\) ---> negative \(4x\) plus \(3y\) equals negative eighteen

The answer is the option D

Step-by-step explanation:  

Part A) we know that

The equation of a line into point slope for is equal to

\(y-y1=m(x-x1)\)

Find the slope

The formula to calculate the slope between two points is equal to


\(m=\frac{y2-y1}{x2-x1}\)


we have


\(A(3,-2)\ B(6,2)\)


Substitute the values


\(m=\frac{2+2}{6-3}\)  

\(m=\frac{4}{3}\)  

With the slope m and the point A find the equation of the line

\(y+2=\frac{4}{3}(x-3)\) -----> equation of the line into point slope form

Part B) we know that

The equation of the line into standard form is equal to

\(Ax+By=C\)

we have

\(y-2=\frac{4}{3}(x-6)\) ------> convert to standard form

\(y=\frac{4}{3}x-8+2\)

\(y=\frac{4}{3}x-6\)

Multiply by \(3\) both sides

\(3y=4x-18\)    

\(-4x+3y=-18\) ----> equation of the line in standard form

Related Questions