Find the value of p if the line which passes through (-1, -p) and…
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Find the x - coordinate of a Point on a Line Given by its Equation
Find the value of p if the line which passes through (-1, -p) and (-2,2) is parallel to the line 2y +8x – 17=0?
The value of p if the line which passes through (-1, -p) and (-2,2) is parallel to the line 2y + 8x – 17 = 0 will be 2.
- If two lines are parallel, then their gradient (also known as slope or dy/dx) will be the same.
- If two lines are perpendicular to each other, then the gradient of one will be the negative inverse of the gradient of the other.
Now, we were told that the two lines are parallel, thus:
The gradient of line 1 = gradient of line 2
The gradient of line 2 will be obtained by making y the subject of the formula and then obtaining the coefficient of x as the gradient.
Recall that for a straight line, y = mx + c,
m = gradient of the line,
c = intercept at y-axis.
So, making y the subject in the equation 2y + 8x – 17 = 0, we have:
2y + 8x – 17 = 0
2y = -8x + 17
y = -8x/2 + 17/2
y = -4x + 8.5
therefore, m = -4, the gradient of line 2 = -4
the gradient of line 1 is also = -4.
Solving for the gradient of line 1, we have:
Given the points: (x₁, y₁) and (x₂, y₂), the gradient between them will be:
= (y₂ – y₁)/(x₂ – x₁)
From the question, y₁ = -p, y₂ = 2, x₁ = -1, x₂ = -2
Thus, substituting, we have
Gradient of line 1 = (y₂ – y₁)/(x₂ – x₁)
= (2 – (-p))/((-2) – (-1))
= (2 + p)/(-2 + 1)
= (2 + p)/-1
= -2 – p
Since gradient of line 1 = gradient of line 2,
-2 – p = -4
– p = – 4 + 2
– p = – 2
P = 2
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is not correct.
- C is not correct.
- D is the correct answer.
You may please note these/this:
- If two lines are parallel, then their slope/gradient is the same.
- If one line is perpendicular to another line, then the gradient/slope of one is negative the inverse of the other.
- For parallel lines, m₁ = m₂. where m = gradient.
- For perpendicular lines, m₂ = -1/m₁.
- The general equation of a straight line is given as y = mx + c. where m = gradient/slope of the line, and c = intercept on the y axis.
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/ culled from 2021 JAMB-UTME MATHEMATICS question 6 /