Answer:
y= 2.5x -4
Step-by-step explanation:
1. Rearrange the equation so that it is in the form y = mx + c.
Add 5x to both sides:
-5x + 5x + 2y= 12 + 5x
2y= 5x + 12
Divide both sides by two:
2y/2= 5x/2 + 12/2
y= 2.5x + 6
2. Find the gradient of the line.
The gradient of the line is the coefficient (the number in front of) x.
For this line, it would be 2.5. (y= 2.5x + 6)
3. Start an equation for the parallel line.
Parallel lines have the same gradients.
This means that we know that the equation we are looking for will be:
y= 2.5x + c
4. Substitute in the values of x and y we have been given.
Coordinates come in the form (x, y), which means we know the values of x and y for one point. So, when x= 10, y=21.
We can substitute these into the equation we have started.
21= 2.5 x 10 + c
21= 25 + c
5. Solve for c.
Subtract 25 from both sides of the equation:
21- 25= 25- 25 + c
-4= c
6. Form the final equation.
The equation of the line parallel to -5x+2y=12 that passes through (10, 21) is:
y= 2.5x -4
