To determine which equations represent a line that is perpendicular to y = -x + 3 and passes through the point (4, 12), we need to find the equation(s) with a slope that is the negative reciprocal of the slope of y = -x + 3.
The given equation is in slope-intercept form y = mx + b, where m represents the slope.
The slope of y = -x + 3 is -1. The negative reciprocal of -1 is 1.
Now let's analyze each equation:
Oy = 5x + 7: The slope of this equation is 5, which is not the negative reciprocal of the slope of y = -x + 3. Therefore, Oy = 5x + 7 is not perpendicular to y = -x + 3.
Oy = x + 15: The slope of this equation is 1, which is the negative reciprocal of the slope of y = -x + 3. Therefore, Oy = x + 15 is perpendicular to y = -x + 3.
0_5x + y = 7: To determine the slope of this equation, we need to rearrange it into slope-intercept form y = mx + b. Subtracting 0.5x from both sides, we get y = -0.5x + 7, which has a slope of -0.5. The negative reciprocal of -0.5 is 2. Therefore, 0.5x + y = 7 is not perpendicular to y = -x + 3.
Based on the analysis, the correct equation representing a line that is perpendicular to y = -x + 3 and passes through the point (4, 12) is:
- Oy = x + 15