Use point-slope form to write the equation of a line that passes through the point \( (-7,1 \) slope -5 .

To write the equation of a line in point-slope form, you can use the formula \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is the point on the line and \( m \) is the slope. For this problem, plug in the point \( (-7, 1) \) and the slope \( -5 \): \[ y - 1 = -5(x + 7) \] This gives you the point-slope equation: \( y - 1 = -5(x + 7) \). Now, shifting gears, did you know that the concept of slope has a fascinating history? Ancient civilizations, like the Greeks, studied the steepness of slopes in their architectural designs, leading to the foundations of geometry. The term “slope” didn’t even arise until the 18th century, showcasing how essential yet underappreciated this mathematical concept has been through time. Speaking of real-world applications, you can find slope equations everywhere! Engineers use them to design roads and ramps, ensuring safe inclines for cars and people alike. Architects rely on slope to create buildings that drain rainwater effectively. So the next time you drive up a hill or walk into a building, just think of the point-slope form working behind the scenes to keep things safe and functioning smoothly!