Final Answer:
The slope-intercept form of the equation of the line that passes through the point (4,3) and is parallel to y = 2x + 1 is y = 2x - 5.
So, none of the option is correct.
Step-by-step explanation:
To find the slope-intercept form of the equation of the line that passes through the point (4, 3) and is parallel to y = 2x + 1, we can follow these steps:
Step 1: Identify the slope of the given line.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. For the given line y = 2x + 1, the slope (m) is 2.
Step 2: Since parallel lines have the same slope, the slope of the line we want to find will also be 2.
Step 3: Use the point-slope form of the line to find the equation.
The point-slope form of a line's equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We want our line to pass through (4, 3), which means that x1 = 4 and y1 = 3.
Step 4: Plug the point and the slope into the point-slope form.
y - 3 = 2(x - 4)
Step 5: Simplify the equation to get it into the slope-intercept form (y = mx + b).
y - 3 = 2x - 8 (Distribute the slope through the parentheses)
y = 2x - 8 + 3 (Add 3 to both sides to isolate y)
y = 2x - 5 (Combine the constants)
Therefore, the slope-intercept form of the equation of the line that passes through the point (4,3) and is parallel to y = 2x + 1 is y = 2x - 5.
None of the option is correct.