Final answer:
The gradient (slope) of the linear equation y = 5x + 7 is 5, and the y-intercept is 7. These values indicate the rate of change of the dependent variable and the point where the line crosses the y-axis, respectively.
Step-by-step explanation:
The student asked to write down the gradient and y-intercept of the linear equation y = 5x + 7.
In the context of linear equations, the general form is often expressed as y = mx + b, where m represents the gradient, or slope, and b represents the y-intercept. The slope of a linear equation is the rate at which the dependent variable (y) changes with respect to the independent variable (x). In the student's equation, the coefficient of x (which is 5) directly indicates the slope. Therefore, the slope (gradient) is 5.
Additionally, the constant term in the equation, which is 7 in this case, represents the y-intercept. This is the value of y when x equals zero, or simply put, where the line crosses the y-axis on a graph. Thus, the y-intercept is 7.
To summarize, the gradient (slope) of the equation y = 5x + 7 is 5, and the y-intercept is 7. Understanding these components is crucial as they determine the shape and position of the line on a graph.