Final answer:
A line parallel to the one described by the equation 3x-2y=4 would have a slope of 1.5, as parallel lines share the same slope.
Step-by-step explanation:
A student has asked, “A line parallel to the above line would have a slope of what for 3x-2y=4.”
To find the slope of a line parallel to the given equation, we first need to rewrite the equation in slope-intercept form (y=mx+b), where m represents the slope and b represents the y-intercept. For the equation 3x-2y=4, we solve for y to find the slope:
- Subtract 3x from both sides: -2y=-3x+4.
- Divide by -2 to solve for y: y=1.5x-2.
The slope of the line described by 3x-2y=4 is 1.5. Since parallel lines have the same slope, a line parallel to the given line also has a slope of 1.5.
This concept relates to slope and the algebra of straight lines where understanding that the m term represents the slope is crucial. Parallel lines having the same slope is a fundamental concept in algebra and coordinate geometry.