Find an equation in slope-intercept form of the line passing through (0, 1) which is parallel to the line y = 6x – 23
m = 6
1 = 6 (0 ) + b
so
b = 1
so
y = 6 x + 1
To find an equation in slope-intercept form for a line parallel to the given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 6 (the coefficient of x in the equation y = 6x - 23). Therefore, the parallel line we need to find will also have a slope of 6.
Using the point-slope form of a linear equation, we can now find the equation of the parallel line passing through the point (0, 1). The point-slope form of a linear equation is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Substituting the values of the given point and slope, we have:
y - 1 = 6(x - 0)
Simplifying the equation:
y - 1 = 6x
Thus, the equation in slope-intercept form of the line passing through (0, 1), which is parallel to the line y = 6x - 23, is y = 6x + 1.