Find an equation in slope-intercept form of the line passing through (0, 1) which is parallel to the line y = 6x – 23
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To find the equation of a line parallel to another line, you need to determine their slopes. The given line has a slope of 6 because it is in the form y = mx + b, where m is the slope.
Since the line we are looking for is parallel, it will also have a slope of 6.
Now that we know the slope, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (0, 1). The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents the coordinates of the given point, and m is the slope.
Substituting the values into the equation, we have:
y - 1 = 6(x - 0)
To simplify the equation, we can distribute 6 to the expression (x - 0):
y - 1 = 6x - 0
Therefore, the equation of the line passing through (0, 1) and parallel to y = 6x - 23 is:
y = 6x + 1.