Write an equation of the line that passes through the point (-1,3) and is parallel to the line y=2x+1. `` I keep getting 2x-1/3 but my teacher said that was wrong.

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baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

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The equation of a line that is parallel to `y = 2x + 1` must have the same slope.  Since `y=2x + 1` is written in slope-intercept form `(y=mx+b)` the slope (m) is 2.

To pass through the point (-1,3) we can use the point slope form for the equation of the line.

Point-slope form: `y - y_(1)= m(x - x_1)`

This gives us the equation: `y - 3 = 2(x - (-1))`

`y - 3 = 2(x+1)`

`y - 3 = 2x + 2`

`y = 2x + 5`

The solution is y = 2x + 5.

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

You need to find the equation of a line passing through (-1,3) and one that is parallel to the line y=2x+1.

First, determine the slope of the line y = 2x + 1. Parallel lines have an equal value for their slope.

y = 2x + 1 is in the form y = m*x + b where m is the slope. Here it is 2.

The equation of a line passing through a point (a, b) and with slope m is (y - b)/(x - a) = m

Substituting the values of a, b and m

(y - 3)/(x + 1) = 2

y - 3 = 2*(x +1)

y - 3 = 2x + 2

y = 2x + 5

The correct equation is y = 2x + 5.

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