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

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

[tex]\text {Slope = } \dfrac{Y_2-Y_1}{X_2-X_1} [/tex]

[tex]\text {Slope = } \dfrac{2+3}{5+1} = \dfrac{5}{6} [/tex]

Write equation with the slope found:

[tex]y = mx + b[/tex]

[tex]y = \dfrac{5}{6} x + b[/tex]

Find y-intercept:

[tex]y = \dfrac{5}{6} x + b[/tex]

[tex]2 = \dfrac{5}{6} (5) + b[/tex]

[tex]2 = \dfrac{25}{6} + b[/tex]

[tex]b = 2 - \dfrac{25}{6}[/tex]

[tex]b = -\dfrac{13}{6}[/tex]

Form the equation:

[tex]y = \dfrac{5}{6} x - \dfrac{13}{6}[/tex]

[tex]\boxed {\boxed {\bf \text {Answer: Line AB : }y = \dfrac{5}{6} x - \dfrac{13}{6}}}[/tex]


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

[tex]\text {Slope of MN = Slope of AB = } \dfrac{5}{6}[/tex]

Write equation with the slope found:

[tex]y = mx + b[/tex]

[tex]y = \dfrac{5}{6} x + b[/tex]

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

[tex]y = \dfrac{5}{6} x + b[/tex]

[tex]-2 = \dfrac{5}{6} (6) + b[/tex]

[tex]-2 =5 + b[/tex]

[tex]b = -2 - 5[/tex]

[tex]b = -7[/tex]

[tex] \boxed {\boxed {\bf \text {Answer: Line MN } : y = \dfrac{5}{6} x -7 }}[/tex]