Write an equation of the line that passes through (2,7) and is parallel to (-2,-2) and (1,4).

Question

please help!!! i need to figure this out!!! : )

Answer 1

Write an equation of the line that passes through (2,7) and is parallel to (-2,-2) and (1,4).

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Since you are given a point (2,7), you can use the point slope form of a line to write the equation.

However where is the slope? Parallel lines have the same slope..........so.......

point slope form would look like this

y- y₁ = m (x - x₁) where m is the slope (x_1,y₁) is a point on the line we have......

y-7 = m (x - 2)......m is the unknown slope....But we do know it is parallel to the line that passes through 2 points

----------------if you have those two points...you have the slope see...... m = (y- y₁)/(x - x₁)

. m = (y- y₁)/(x - x₁) = (4-(-2))/(1-(-2)) = 6/3 = 2.....m=2.....so......

y-7 = m (x - 2)......put your slope in...you have.....y-7=2(x-2) in point slope format....

Answer 2

Don't fret!!!

Parallel lines have the SAME slope. Find the slope of the line that passing through (-2, 2) & (1, 4)

m = change in y / change in x = (4 - 2)/(1 - (-2)) = 2/3

Doesn't matter which point you make P1 and P2, the slope will be the same.

Then use the POINT-SLOPE formula and plug in the 1st point given (that you want the equation for) and the slope (m) you just calculated...

y - y1 = m (x - x1)

y - 7 = (2/3)(x - 2)

y - 7 = (2/3)x - (2/3)(-2)

y - 7 = 2/3x + 4/6

Bring the 7 over to the RHS to isolate the y

y = 2/3x + 4/6 + 7

You need a common denominator to add 4/6 and 7 (fraction and whole #)...here its 6. Multiply 7 by (6/6)

You will be adding 4/6 + 42/6

y = 2/3x + 48/6 (factor the 6 into the 48 to put this term in its lowest term)

y = 2/3x + 8

Hope this helps...