Question

Find the equation of the straight line:

Which passes through the point (3,-1) and is parallel to the straight line passing through the two points (1,5) and (-2,1) ​

Answer 1

`y=(4)/(3) x-5`

Explanation:

1. Find the slope of the line using the information given about the line it is parallel to.

• When lines are parallel to one another, that means they have the same slope. Therefore, if we find the slope of the parallel line, we find the slope of the line we're solving for.
• Find the slope of the line by using the equation
  `m=(y_2-y_1)/(x_2-x_1)`.
• Choose and identify which pair of points is which; let's say that
  `(x_1, y_1)=(1,5)` and
  `(x_2, y_2)=(-2,1)`. You don't want to accidentally calculate for
  `m=(y_1-y_2)/(x_2-x_1)` instead... don't get the numbers mixed up!
• Plug the coordinates into the equation correctly:
  `m=(1-5)/(-2-1)`
• Solve the equation:
  `m=(-4)/(-3) =(4)/(3)`
• The slope is 4/3.

2. Solve for b by using the coordinate our line passes through and our calculated slope.

• The equation for a line is
  `y=mx+b`.
• Note the information that we have about our line:
  `m=(4)/(3)`
• Also, because we are given coordinates, we can use those points to plug in for y and x. Therefore, for the purpose of solving for b,
  `x=3` and
  `y=-1`.
• Plug the information we have into the formula and then solve for b:
  `-1=(4)/(3)(3)+b`
• Multiply 4/3 and 3:
  `-1=4+b`
• Subtract both sides by 4:
  `b=-5`

3. Plug in the information for slope (m), and y-intercept (b), into the equation for a line.

• 
  `y=(4)/(3) x-5`