# Find the value of p if the line which passes through (-1, -p) and…

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**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?**

**A.**** −2****/****7**

**B.**** 7****/****6**

**C.**** −6****/****7**

**D.**** 2**

**QUICK ANSWER…**

**D**

**DETAILS…**

**T****he 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.**

**Recall that:**

**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.**

**KEY-POINTS…**

**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 20****21**** JAMB-UTME**** MATHEMATICS**** question**** 6 ****/**