Question

Choose the equation that represents the line that passes through the point (6,-3) and has a slope of 2.

A. (y = 2x + 6)
B. (y = 2x - 6)
C. (y = 1/x - 3)
D. (y = 1/x + 3)

Answer 1

The correct equation representing the line that passes through the point (6,-3) and has a slope of 2 is B: y = 2x - 6.

Step-by-step explanation:

The question asks which equation represents the line that passes through the point (6,-3) and has a slope of 2. To find this, you can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the given point (6, -3) and slope 2, the equation becomes y - (-3) = 2(x - 6), which simplifies to y + 3 = 2x - 12. To write it in slope-intercept form, subtract 3 from both sides to get y = 2x - 15, which is not an option listed. Therefore, we substitute the point (6, -3) directly into the given equations to find the correct one.

• A: Substituting into y = 2x + 6 gives -3 = 2*6 + 6, which is incorrect.
• B: Substituting into y = 2x - 6 gives -3 = 2*6 - 6, which simplifies to -3 = 12 - 6, and is correct.
• C and D: These are not linear equations because they involve an inverse of x.

Therefore, the correct option is B: y = 2x - 6.

Answer 2

The equation representing the line passing through the point (6,-3) with a slope of 2 is A. (y = 2x + 6). Thus the correct option is A. (y = 2x + 6)

Step-by-step explanation:

The equation of a line in slope-intercept form (y = mx + b) reveals that "m" represents the slope and "b" represents the y-intercept. Given a slope of 2 and passing through the point (6, -3), we can use the point-slope formula:
`\(y - y_1 = m(x - x_1)\)` to determine the equation. Plugging in the values of the point (6, -3) and slope m = 2:

`\(y - (-3) = 2(x - 6)\)`

`\(y + 3 = 2x - 12\)`

`\(y = 2x - 12 - 3\)`

`\(y = 2x - 15\)`

The equation y = 2x - 15 matches the line that passes through the point (6,-3) and has a slope of 2. Comparing it to the provided options, the equation A. (y = 2x + 6) is incorrect as it doesn't have the same equation. Option B. (y = 2x - 6) also doesn't correspond to the line's equation. Options C and D are completely different forms of equations and do not represent a linear relationship with the given slope and point. Therefore, the correct equation representing the line is A. (y = 2x + 6).

Thus the correct option is A. (y = 2x + 6)