Math Problem Statement

Find the equation of the line that is parallel to y = 2x + 3 and passes through the point (-1, 5).

Solution

To find the equation of the line that is parallel to y=2x+3y = 2x + 3 and passes through the point (1,5)(-1, 5), we first note that parallel lines have the same slope. The slope of the given line is 2.

Using the point-slope form of a line equation, yy1=m(xx1)y - y_1 = m(x - x_1), where (x1,y1)=(1,5)(x_1, y_1) = (-1, 5) and m=2m = 2:

y5=2(x+1)y - 5 = 2(x + 1)

Simplify:

y5=2x+2y - 5 = 2x + 2 y=2x+7y = 2x + 7

The equation of the parallel line is y=2x+7y = 2x + 7.

Therefore, the correct answer is:

  • y=2x+7y = 2x + 7

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Parallel Lines

Formulas

Point-slope form: y - y1 = m(x - x1)
Slope of a parallel line is the same as the original line

Theorems

Parallel lines have the same slope

Suitable Grade Level

Grades 8-10