A student found the slope of a line that passes through the points (1, 14) and (3, 4) to be 5. What mistake did she make ?
1 answer:
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Answer: x=12
Step-by-step explanation:
1. Accoding to the Side-Splitter Theorem, if a line interesect two sides of the triangle and it is parallel to the third side, then the other two sides are divided by the line proportionally.
2. Then, you can form the following proportion:
3. Substitute values and solve for x:
a = 1, b =14 and y-coordinate is 6 when x = 0.
Solution:
Let us first write the equation of a line.
Take the points are (2, 2) and (6, 10).
Slope of the line:
m = 2
Point-slope formula:
y - 10 = 2(x - 2)
y - 10 = 2x - 4
Add 10 on both sides,we get
y = 2x + 6
Equation of a line is y = 2x + 6.
To find (a, 8), substitute x = a and y = 8 in the equation,
8 = 2a + 6
Subtract 6 from both sides, we get
2 = 2a
a = 1
To find (4, b), substitute x = 4 and y = b in the equation,
b = 2(4) + 6
b = 8 + 6
b = 14
Substitute x = o in the equation.
y = 2(0) + 6
y = 6
The y-coordinate is 6 when x = 0.