Question

Given the points A(-1,-3) and B(5,2). A. Write the equation of the straight line AB. Another line MN is parallel to AB and passes through the point (6,-2). B. Write the equation of the straight line MN

Answer 1

Find slope of AB where A = (-1,-3) and B = (5,2):

$\text {Slope = } \dfrac{Y_2-Y_1}{X_2-X_1}$

$\text {Slope = } \dfrac{2+3}{5+1} = \dfrac{5}{6}$

Write equation with the slope found:

$y = mx + b$

$y = \dfrac{5}{6} x + b$

Find y-intercept:

$y = \dfrac{5}{6} x + b$

$2 = \dfrac{5}{6} (5) + b$

$2 = \dfrac{25}{6} + b$

$b = 2 - \dfrac{25}{6}$

$b = -\dfrac{13}{6}$

Form the equation:

$y = \dfrac{5}{6} x - \dfrac{13}{6}$

$\boxed {\boxed {\bf \text {Answer: Line AB : }y = \dfrac{5}{6} x - \dfrac{13}{6}}}$


Find Slope of Line  MN where MN is parallel to AB:

$\text {Slope of MN = Slope of AB = } \dfrac{5}{6}$

Write equation with the slope found:

$y = mx + b$

$y = \dfrac{5}{6} x + b$

Find y-intercept given that the line passed through (6, -2):

$y = \dfrac{5}{6} x + b$

$-2 = \dfrac{5}{6} (6) + b$

$-2 =5 + b$

$b = -2 - 5$

$b = -7$

$\boxed {\boxed {\bf \text {Answer: Line MN } : y = \dfrac{5}{6} x -7 }}$