Asked by Lauren Pennetta on May 06, 2024
Verified
Write an equation of the line that passes through (−8,52) \left( - 8 , \frac { 5 } { 2 } \right) (−8,25) and has a slope of m=16m = \frac { 1 } { 6 }m=61 .
A) −x+6y=−38- x + 6 y = - 38−x+6y=−38
B) −x+y=−38- x + y = - 38−x+y=−38
C) x+6y=−41x + 6 y = - 41x+6y=−41
D) −x+6y=23- x + 6 y = 23−x+6y=23
E) −x+6y=−23- x + 6 y = - 23−x+6y=−23
Slope
The measure of the steepness or incline of a line, defined as the ratio of the vertical change to the horizontal change.
Equation
A mathematical statement that asserts the equality of two expressions, often including variables and constants.
Point
A singular location in space that can represent a position on a graph or in a geometric context.
- Find the equation representing a line with an identified point and slope.
- Frame the equation of a line in its general structure.
Verified Answer
FB
Francy BlancMay 07, 2024
Final Answer :
D
Explanation :
We can use point-slope form to start:
y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1=m(x−x1)
where (x1,y1)=(−8,5/2)(x_1, y_1) = (-8, 5/2)(x1,y1)=(−8,5/2) and m=1/6m = 1/6m=1/6 . Plugging in these values, we get
y−52=16(x+8)y - \dfrac{5}{2} = \dfrac{1}{6}(x + 8)y−25=61(x+8)
Multiplying both sides by 6 to get rid of the fraction, we get
6y−15=x+86y - 15 = x + 86y−15=x+8
Rearranging, we get
x−6y=−23x - 6y = -23x−6y=−23
So the answer is (D).
y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1=m(x−x1)
where (x1,y1)=(−8,5/2)(x_1, y_1) = (-8, 5/2)(x1,y1)=(−8,5/2) and m=1/6m = 1/6m=1/6 . Plugging in these values, we get
y−52=16(x+8)y - \dfrac{5}{2} = \dfrac{1}{6}(x + 8)y−25=61(x+8)
Multiplying both sides by 6 to get rid of the fraction, we get
6y−15=x+86y - 15 = x + 86y−15=x+8
Rearranging, we get
x−6y=−23x - 6y = -23x−6y=−23
So the answer is (D).
Learning Objectives
- Find the equation representing a line with an identified point and slope.
- Frame the equation of a line in its general structure.
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