Mathematics 2018 JAMB Past Questions - Question 38: Find the equation of the line through (5,7) parallel to the line 7x +5y = 12

Correct Answer

B

Explanation

Equation through (5,7) parallel to the line7x +5y = 125y = - 7x + 12 = y = -7x /5 +12 /5Gradient = -7therefor Required equation = y -7 /x -5 = -7 /5i.e. 5y - 35 = -7x +355y +7x =70To find the equation of the line through the point (5,7) that is parallel to the line 7x + 5y = 12, we can follow these steps:Step 1: First, we need to find the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. We need to rearrange the given line equation into this form.7x + 5y = 125y = -7x + 12y = (-7/5)x + 12/5So, the slope of the given line is -7/5.Step 2: Since the line we want to find is parallel to the given line, it will have the same slope. The slope of the line we want to find is also -7/5.Step 3: Now we can use the point-slope form of a line to find the equation of the line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.Using the point (5,7) and the slope -7/5, we get:y - 7 = (-7/5)(x - 5)Step 4: We can simplify this to get the equation in slope-intercept form.y - 7 = (-7/5)x + 7y = (-7/5)x + 7 + 7y = (-7/5)x + 14So, the equation of the line through the point (5,7) that is parallel to the line 7x + 5y = 12 is y = (-7/5)x + 14.