Helena wrote the equation using point-slope form for the line that passes through the points (5, 1) and (3, 5). Analyze the steps of her work using the point-slope form to write the equation.
1. m = Start Fraction 5 minus 1 Over 3 minus 5 End Fraction = Start Fraction 4 Over negative 2 End Fraction = negative 2. 2. y minus 1 = negative 2 (x minus 3). Y minus 1 = negative 2 x + 6. y minus 1 + 1 = negative 2 x + 6 + 1. 3. y = negative 2 x + 7.
In which step did Helena make an error?
In step 1, she substituted the x values for y and the y values for x.
In step 2, she didn’t use an x and y from the same coordinate pair.
In step 3, she solved for the wrong variable.
Helena did not make an error.
Answers
Answer:
The correct option is B. In step 2, she didn’t use an x and y from the same coordinate pair.
Step-by-step explanation:
Consider the provided points:
(5, 1) and (3, 5)
We need to find the equation of line using point slope form.
m=\frac{y_2-y_1}{x_2-x_1}m=
x
2
−x
1
y
2
−y
1
Substitute \left(x_1,\:y_1\right)=\left(5,\:1\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)(x
1
,y
1
)=(5,1),(x
2
,y
2
)=(3,5) in above formula.
Step 1:
m=\frac{5-1}{3-5}=\frac{4}{-2}=-2m=
3−5
5−1
=
−2
4
=−2
(y-y_1)=m(x-x_1)(y−y
1
)=m(x−x
1
)
Substitute the respective values in the above formula.
Step 2:
(y-1)=-2(x-5)(y−1)=−2(x−5)
y-1=-2x+10y−1=−2x+10
y=-2x+11y=−2x+11
Now consider the provided steps.
Here, we can observed that Helena made mistake in step 2 she didn’t use an x and y from the same coordinate pair.
Hence, the correct option is B. In step 2, she didn’t use an x and y from the same coordinate pair.
Answer:
option b
Step-by-step explanation: