A line has a slope of 121 and passes through the point (3,721).
Which expression corresponds to the line?
To solve the problem of finding the equation of the line:
- Step 1: Identify the given information: slope m=121=23, and point (x1,y1)=(3,721)=(3,215).
- Step 2: Use the point-slope formula y−y1=m(x−x1).
- Step 3: Substitute the given slope and point into the formula: y−215=23(x−3).
- Step 4: Distribute the slope on the right side: y−215=23x−29.
- Step 5: Add 215 to both sides to solve for y: y=23x−29+215.
- Step 6: Simplify the right side: y=23x+3.
- Step 7: Compare this expression to the provided choices to find a match. The form is the same as choice y=121(x+2), rewritten correctly as y=23(x+2).
Therefore, the expression that corresponds to the line is y=121(x+2).
y=121(x+2)