What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
y = 5x - 3 is the equation of a line with a slope of 5 that passes through the point (-2, -7).
To find the equation of the line, we can use the point-slope formula \(y - y_1 = m(x - x_1)\) where \(m\) is the slope and \((x_1, y_1)\) is the point on the line. Substituting in the slope of 5 and the point (-2, -7) gives us the correct equation.
This equation has a y-intercept of +3, which does not correspond to the point (-2, -7). Substituting x = -2 into this equation yields y = 5(-2) + 3 = -10 + 3 = -7, which is incorrect since we need the y-coordinate to be -7 at that x-coordinate.
While this equation has the correct slope of 5, substituting the point (-2, -7) yields y = 5(-2) - 3 = -10 - 3 = -13. This does not equal -7, confirming that this equation does not pass through the given point.
This equation has the correct slope of 5. When substituting the point (-2, -7), we find y = 5(-2) - 17 = -10 - 17 = -27, which does not match the required y-coordinate of -7. Therefore, this choice is also incorrect.
This equation also has the correct slope of 5, but the y-intercept is +17. Substituting (-2, -7) gives y = 5(-2) + 17 = -10 + 17 = +7, which does not equal -7. Hence, it fails to satisfy the condition of passing through the point.
Finding the equation of a line requires both the correct slope and the point it passes through. In this case, the line with slope 5 that passes through (-2, -7) can be accurately determined using the point-slope formula, resulting in the equation y = 5x - 17. All other options provided either fail to maintain the correct slope or do not intersect with the specified point on the graph.
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