Question

Write the equation of the line that is parallel to the line y = 2x + 2 and passes through the point (5, 3)?

Answer 1

for two lines to be parallel they need to have the same slope. if your linear equation (equation of a line has highest exponent equal to one) is in the slope intercept form y=mx+b then m is your slope. your equation is in slope intercept form y=2x+2 so your slope m is equal to 2. so far you have the equation of a line y=2x+b you need to find b.
well, plug in the point you want to be on the line, for a point to be on the line is the same as saying it is a solution of the equation y=2x+b so that is why you plug it in. (5,3) you have x=5 and y=3 so y=2x+b becomes 3=2(5)+b solving for b you have 3-10=b, so -7=b so your desired equation would be y=2x-7

Answer 2

the slope of the equation is 2...it says parallel line so slope of parallel is also 2

now use \(y - y_1 = m(x-x_1)\)

substitute the values

y - 3 = 2(x-5)

y - 3 = 2x - 10

2x - y - 10 + 3 = 0

can you simplify that?

Answer 3

y=2x-7