Question

write the equation of the line that is parallel to x-3y=-12 and passes through the point (6,5)

Answer 1

parallel lines have the same slope... solve for y first, use the coefficient of your x variable as the slope for your new equation, and then calculate where your appropriate y-intercept based off of your slope going through the (6,5) point.

Answer 2

rewrite the equation so it is y = .........
once you have done that you will see it has the form

y=mx+c where m and c are constants

This is the general form for a straight line, and tells oyu exactly about the line.

the value of m is the slope, or gradient of the line.

Now - it is true, and fairly evident when oyu look at the graph, that any line that is parallel to it will have the SAME slope.

SO for the new line you know the 'm' for the formula.

You also know 1 point on the line, so you can put the coordinates of that point into the equation.

5=6m+c and since you know m you can calculate c

so now oyu have the full formula for the new line - it has the SAME slope as the line given - but a different value of c