Final answer:
The equation of the line that passes through the point (3, – 2) and is parallel to the line y = ½x - 2 is y = ½x - 2¾.
Step-by-step explanation:
To find the equation of a line that passes through the coordinate (3, – 2) and is parallel to the line given by the equation y = ½x – 2, you need to identify the slope of the line to which it is parallel. In this case, the slope is ½, which is represented by the coefficient of x in the equation. Since parallel lines have the same slope, the line we are looking for will have the same slope of ½.
To find the specific equation of this parallel line, we use the point-slope formula, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Substituting the known values, we have (y + 2) = ½(x - 3). Simplifying this, we get:
y + 2 = ½x - ¾
y = ½x - ¾ - 2
y = ½x - ¾ - ¾
y = ½x - 2¾
This is the equation of the line that passes through the point (3, – 2) and is parallel to the line y = ½x - 2.