Mathematics 2014 JAMB Past Questions - Question 36: Find the equation of the straight line through (-2,3) and perpendicular to 4x+3y-5=0

Correct Answer

B

Explanation

4x + 3y - 5 = 0 (given)the equation of the line perpendicular to the given line takesthe form 3x - 4y = kThus, substituting x = - 2 and y = 3 in 3x - 4y = kTo find the equation of a straight line perpendicular to the given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.First, let's rewrite the given line in the slope-intercept form (y = mx + c), where m is the slope and c is the y-intercept:4x + 3y - 5 = 03y = -4x + 5y = (-4/3)x + 5/3From this equation, we can see that the slope of the given line is -4/3.The negative reciprocal of -4/3 is 3/4. This will be the slope of the line perpendicular to the given line.Now, we can use the point-slope form of a straight line to find the equation of the line passing through the point (-2, 3) with a slope of 3/4:y - y1 = m(x - x1)Substituting the values (-2, 3) and m = 3/4 into the equation, we get:y - 3 = (3/4)(x - (-2))Simplifying further:y - 3 = (3/4)(x + 2)Multiplying both sides of the equation by 4 to eliminate the fraction, we have:4(y - 3) = 3(x + 2)Expanding the equation:4y - 12 = 3x + 6Rearranging the equation to the standard form:3x - 4y + 18 = 0Therefore, the equation of the straight line passing through (-2, 3) and perpendicular to 4x + 3y - 5 = 0 is 3x - 4y + 18 = 0.G ives 3 (-2) -4 (3) = k - 6 - 12 = k therefore k = -18Hence the required equation is 3x - 4y = - 183x - 4y +18 = 0To find the derivative of y = 4x³ - 2x² + x with respect to x (dy/dx), we can apply the power rule and the sum rule of differentiation.The power rule states that if we have a term of the form ax^n, the derivative with respect to x is given by nx^(n-1).Using the power rule, we can find the derivative of each term in the given equation:dy/dx = d/dx (4x³) - d/dx (2x²) + d/dx (x)Applying the power rule to each term, we get:dy/dx = 12x² - 4x + 1Therefore, the derivative of y = 4x³ - 2x² + x with respect to x is dy/dx = 12x² - 4x + 1.