Consider a line that passes through the point (−2,3) and is parallel to the line with equation 3x−2y=5. Which choice represents an equation of this line?
Two lines are parallel if and only if their slopes are equal. The line with equation 3x - 2y = 5 can be rewritten in slope-intercept form as y = (3/2)x - 5/2.
Therefore, the slope of this line is 3/2.
Since the line we are looking for is parallel to this line, it will also have a slope of 3/2.
We can then use the point-slope form of the equation of the line to determine the equation.
The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Plugging in the point (-2, 3) and the slope 3/2 into the equation, we get:
y - 3 = (3/2)(x - (-2))
Simplifying, we have:
y - 3 = (3/2)(x + 2)
Multiplying the slope through, we get:
y - 3 = (3/2)x + 3
Adding 3 to both sides, we have:
y = (3/2)x + 6
Therefore, the equation of the line that passes through (-2, 3) and is parallel to the line 3x - 2y = 5 is y = (3/2)x + 6.