Asked by Kimberly Zayas-Maciel on May 16, 2024
Verified
Write an equation of the line that passes through the points (−1,1.6) ( - 1,1.6 ) (−1,1.6) and (−3,−4.4) ( - 3 , - 4.4 ) (−3,−4.4) . Write the equation in general form.
A) x−3y−4.6=0x - 3 y - 4.6 = 0x−3y−4.6=0
B) 3x+y+5.8=03 x + y + 5.8 = 03x+y+5.8=0
C) −3x+y+5.8=0- 3 x + y + 5.8 = 0−3x+y+5.8=0
D) −3x+y−4.6=0- 3 x + y - 4.6 = 0−3x+y−4.6=0
E) x+3y−4.6=0x + 3 y - 4.6 = 0x+3y−4.6=0
General Form
A standard way of writing something, in mathematics, typically referring to the standard form of an equation.
Points
Refers to specific positions or locations in a geometric space, each defined by coordinates.
Line
An infinitely extending one-dimensional entity without any thickness, known as a line.
- Formulate the equation of a line in its general form.
Verified Answer
KB
Kendall BellamyMay 20, 2024
Final Answer :
D
Explanation :
The equation can be found using the slope-intercept form, which is y=mx+by = mx + by=mx+b where mmm is the slope and bbb is the y-intercept. First, we need to find the slope of the line using the two points:
m=y2−y1x2−x1=−4.4−1.6−3−(−1)=−6−2=3m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4.4 - 1.6}{-3 - (-1)} = \frac{-6}{-2} = 3m=x2−x1y2−y1=−3−(−1)−4.4−1.6=−2−6=3
Now we can use the point-slope form of the equation, substituting one of our given points:
y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1=m(x−x1)
y−1.6=3(x+1)y - 1.6 = 3(x + 1)y−1.6=3(x+1)
Simplifying, we get:
y=3x+4.4y = 3x + 4.4y=3x+4.4
To put it in general form, we can move the constant term to the other side:
−3x+y−4.4=0-3x + y - 4.4 = 0−3x+y−4.4=0
Which matches choice D.
m=y2−y1x2−x1=−4.4−1.6−3−(−1)=−6−2=3m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4.4 - 1.6}{-3 - (-1)} = \frac{-6}{-2} = 3m=x2−x1y2−y1=−3−(−1)−4.4−1.6=−2−6=3
Now we can use the point-slope form of the equation, substituting one of our given points:
y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1=m(x−x1)
y−1.6=3(x+1)y - 1.6 = 3(x + 1)y−1.6=3(x+1)
Simplifying, we get:
y=3x+4.4y = 3x + 4.4y=3x+4.4
To put it in general form, we can move the constant term to the other side:
−3x+y−4.4=0-3x + y - 4.4 = 0−3x+y−4.4=0
Which matches choice D.
Learning Objectives
- Formulate the equation of a line in its general form.
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