Question 5: straight line passes through \( (5,-2) \) and has a gradient of 4 . The equation of the line is

To find the equation of the line that passes through the point \( (5, -2) \) with a gradient (slope) of 4, we can use the point-slope form of a linear equation, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line. Plugging in the values, we get: \[ y - (-2) = 4(x - 5) \] This simplifies to: \[ y + 2 = 4x - 20 \] Finally, bringing everything to one side gives us the equation of the line: \[ y = 4x - 22. \] A straight line can represent many things in real life! For example, it can depict speed—imagine a car moving steadily down a road with a consistent speed. The slope tells you how steep the road is, while the y-intercept shows where the road would cross the vertical axis when the car starts. Simple equations like this help drivers understand their journey! When solving these equations, students often forget to distribute correctly or mix up the signs when subtracting. A classic blunder is miscalculating the y-intercept after moving terms around. Always double-check your steps, and it can help to graph your line to visually confirm that you’ve got it right!