Question

priya and han each wrote an equation of line with a slope of 1/3that passes through the points (1,2) priya's equationis y-2=1/3(x-1) and han's equations is 3y-x=5 do you agree with either of them? explain your reasoning

Answer 1

Both Priya's equation y-2=1/3(x-1) and Han's equation 3y-x=5 are correct; they have the slope of 1/3 and pass through the point (1,2). Han's equation in slope-intercept form also reveals a slope of 1/3, further confirming its correctness.

Step-by-step explanation:

The student's question asks whether Priya's equation y-2=1/3(x-1) or Han's equation 3y-x=5 is correct given the constraints of a slope of 1/3 and passing through the point (1,2). To determine if either equation is correct, one could first put Han's equation into slope-intercept form to compare the slopes directly.

Rearranging Han's equation to solve for y yields:

• Add x to both sides: 3y = x + 5
• Divide all terms by 3: y = 1/3x + 5/3

This shows that Han's equation does indeed have a slope of 1/3, which matches the given slope.

Next, we can check if the point (1,2) satisfies both equations. Substituting x=1 and y=2 into Priya's equation:

• 2 - 2 = 1/3(1-1)
• 0 = 0, which is true.

Now substituting into Han's equation:

• 3(2) - 1 = 5
• 6 - 1 = 5, which is also true.

Both equations satisfy the conditions of having a slope of 1/3 and passing through the point (1,2), so both Priya's and Han's equations are correct.