Final answer:
A line parallel to the given equation, which in slope-intercept form is y = (3/2)x + 5, will have the same slope of 3/2. To write the equation for the parallel line passing through a given point, substitute the point's coordinates into y = (3/2)x + b and solve for b. The equation of the new line will have the form y = (3/2)x + b.
Step-by-step explanation:
To write an equation for a line that passes through a given point and is parallel to another line, you will first need to understand the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. The provided equation, 2y = 3x + 10, can be rewritten in slope-intercept form by dividing each term by 2, resulting in y = (3/2)x + 5.
A line parallel to this will have the same slope, so the slope m will also be 3/2. The equation of the new line will have the form y = (3/2)x + b. To find the new y-intercept b, you can plug in the coordinates of the given point the line must pass through, for example, (x1, y1), into the equation and solve for b.
If the line must pass through the point (1, 4), you would substitute these values into your parallel line equation:
- 4 = (3/2)(1) + b
- 4 = 3/2 + b
- b = 4 - 3/2
- b = 5/2
Thus, the equation of the line parallel to 2y = 3x + 10 passing through the point (1, 4) would be y = (3/2)x + 5/2.
This process can be used for any given point by substituting the corresponding x and y values into y = (3/2)x + b and solving for b.