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 = } (Y_2-Y_1)/(X_2-X_1)`


`\text {Slope = } (2+3)/(5+1) = (5)/(6)`

Write equation with the slope found:


`y = mx + b`


`y = (5)/(6) x + b`

Find y-intercept:


`y = (5)/(6) x + b`


`2 = (5)/(6) (5) + b`


`2 = (25)/(6) + b`


`b = 2 - (25)/(6)`


`b = -(13)/(6)`

Form the equation:


`y = (5)/(6) x - (13)/(6)`


`\boxed {\boxed {\bf \text {Answer: Line AB : }y = (5)/(6) x - (13)/(6)}}`


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


`\text {Slope of MN = Slope of AB = } (5)/(6)`

Write equation with the slope found:


`y = mx + b`


`y = (5)/(6) x + b`

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


`y = (5)/(6) x + b`


`-2 = (5)/(6) (6) + b`


`-2 =5 + b`


`b = -2 - 5`


`b = -7`


`\boxed {\boxed {\bf \text {Answer: Line MN } : y = (5)/(6) x -7 }}`