What is the equation of the line passing through (-1, 4) and parallel to y = 2x + 1?

Solution:

Given, the equation of line is y = 2x + 1

Point (x₁,y₁) = (-1, 4)

The above equation is in slope-intercept form y = mx+c

Where, c = constant term

m = slope

Slope of the line y = 2x + 1 is m = 2

The equation of a line that passes through a point (x₁,y₁) and a slope m is given by

(y - y₁) = m (x - x₁)

Since the line is parallel to y = 2x + 1, slope, m = 2

(y - 4) = 2(x - (-1))

y - 4 = 2(x + 1)

y - 4 = 2x + 2

y = 2x + 2 + 4

y = 2x + 6

Therefore, the equation of the line is y = 2x + 6.

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What is the equation of the line passing through (-1, 4) and parallel to y = 2x + 1?

Summary:

The equation of the line passing through the point (-1,4) and parallel to the line y = 2x + 1 is y = 2x + 6.