A straight line with a slope of 2 passes through the point (7,11).
Which expression corresponds to the line?
To solve this problem, we'll follow these steps:
- Step 1: Identify the given information.
- Step 2: Apply the point-slope formula.
- Step 3: Simplify to match one of the given options.
Now, let's work through each step:
Step 1: The problem gives us the slope m=2y and the point (7,11).
Step 2: Using the point-slope form of a line, y−y1=m(x−x1), we substitute y1=11, m=2y, and x1=7. The equation becomes:
y−11=2y(x−7)
Step 3: Simplify the equation:
- Multiply through: y−11=2yx−14y.
- Rearrange terms to solve for y:
- Start by moving y on one side and other terms on the other: y−2yx=−14y+11.
- Rearranging gives y−11+14y=2yx.
- This rearranges to: 15y=2yx+11.
- Or separating terms appropriately and simplifying: y=3x−3−x.
Therefore, the solution to the problem is y=3x−3−x, which corresponds to choice 4.
y=3x−3−x