Final answer:
The equation of a line with a slope of 7 that passes through the point (5, -3) could be expressed as y = 7x - 38 after using the point-slope form. The provided options do not include this exact equation, but option A has the correct slope and is the closest match despite an incorrect y-intercept.
Step-by-step explanation:
To find the equation of a line with a given slope that passes through a specific point, you can use the point-slope form of the equation which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.
In this case, the line has a slope (m) of 7 and passes through the point (5, -3). Plugging these values into the point-slope formula gives us: y - (-3) = 7(x - 5)
This simplifies to: y + 3 = 7x - 35
Subsequently, to get into the y = mx + b format: y = 7x - 35 - 3 y = 7x - 38
None of the choices provided in the question exactly match this equation. Therefore, there is likely a typo in the provided options, or the question may need revision. However, we can determine which option is closest to the correct equation by identifying the correct slope and seeing which option has the y-intercept closest to -38. Option A y = 7x - 3 has the correct slope but an incorrect y-intercept.