Answer:
Gradient of Line A: 0.75
Gradient of Line B: 0.8
Therefore the lines ARE NOT parallel.
Step-by-step explanation:
Find the gradient (slope) of line A and B respectively.
Line A Gradient:
Equation of line A is 3x - 4y = 5
Rewrite this in slope-intercept form as y = mx + b, where m is the gradient (slope).
Thus,
3x - 4y - 3x = -3x + 5
-4y = -3x + 5
Divide both sides by -4
y = ¾x + ⁵/4
The gradient = ¾ = 0.75
Line B Gradient:
Gradient of line passing through (4, 7) and (-1, 3)
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 7}{-1 - 4} = \frac{-4}{-5} = \frac{4}{5} [/tex]
Gradient (m) = ⅘ = 0.8
Since both lines do not have the same gradient, therefore the lines are not parallel.
