The equation of the line passing through (2, 3) and perpendicular to y = -1/4 * x + 1 is y = 4x - 5.
Step-by-step explanation:
To find an equation of the line passing through the point (2, 3) that is perpendicular to the line y = -1/4 * x + 1, we need to determine the slope of the perpendicular line first. The slope of the given line is -1/4, so the slope of the perpendicular line will be the negative reciprocal, which is 4. We can use the point-slope form of the equation to find the equation of the perpendicular line:
y - y1 = m(x - x1)
Substituting the values (2, 3) for (x1, y1) and 4 for m, we get:
y - 3 = 4(x - 2)
This equation can be simplified and rearranged to find the final equation in slope-intercept form:
y = 4x - 5
Therefore, the equation of the line passing through (2, 3) that is perpendicular to y = -1/4 * x + 1 is y = 4x - 5.