Final answer:
To find an equation of a line that is perpendicular to the given line, we need to determine the slope of the given line first. The slope of the perpendicular line will be the negative reciprocal of the given line's slope.
Step-by-step explanation:
To find an equation of a line that is perpendicular to the line whose equation is 2y + 3x = 1, we need to determine the slope of the given line first.
Let's rewrite the given equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2y + 3x = 1
2y = -3x + 1
y = (-3/2)x + 1/2
Since the slope of the given line is -3/2, the slope of the perpendicular line will be the negative reciprocal of -3/2, which is 2/3. We can then create the equation of the perpendicular line by using the slope-intercept form:
y = (2/3)x + b
Since there is no information given about the y-intercept of the perpendicular line, we don't know the value of b. Therefore, the equation of a line perpendicular to 2y + 3x = 1 can be written as y = (2/3)x + b, where b is a constant value.