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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.
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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