how do you do this math problem

Question

write the equation of the line that is parallel to y=2x+3 and passes through (-6,0)

Answer 1

this equation is written in the form y=mx+b, where m is the slope of the line and b is the y intercept.  The equation y=2x+3 has a slope of 2 because 2 is the coefficient on the x term.  When two lines are parallel, they are increasing or decreasing at the same rate (or slope) and will never intersect one another, therefore if a line is PARALLEL to y=2x+3 then it too has a slope of m=2. We can then use that m value and the coordinate (-6,0) where x=-6 and y=0 to plug them into the form y=mx+b and solve to find b. So, by substitution we would have 0=2(-6) + b, simplifying we would have 0=-12+b, if we add 12 to both sides to isolate b, we would get 12=b. Now we can use the values m=2 and b=12, keep x and y as variables in the equation y=mx+b and get our new equation: y=2x+12. This line is parallel to y=2x+3. Same slope but different y-intercepts.