What is the equation of the line with slope 4 passing through (0, 1)?

The equation of the line with slope 4 passing through (0, 1) is \( y = 4x + 1 \).

To understand how we arrive at this equation, let's break it down step by step. The general form of the equation of a straight line is \( y = mx + c \), where \( m \) represents the slope of the line and \( c \) is the y-intercept, which is the point where the line crosses the y-axis.

In this case, we are given that the slope \( m \) is 4. This means that for every unit increase in \( x \), the value of \( y \) increases by 4 units. Additionally, the line passes through the point (0, 1). The coordinates (0, 1) tell us that when \( x = 0 \), \( y = 1 \). This point is actually the y-intercept \( c \).

Substituting the slope \( m = 4 \) and the y-intercept \( c = 1 \) into the general form of the line equation, we get:
\[ y = 4x + 1 \]

This equation tells us that if you know the value of \( x \), you can find the corresponding value of \( y \) by multiplying \( x \) by 4 and then adding 1. For example, if \( x = 2 \), then:
\[ y = 4(2) + 1 = 8 + 1 = 9 \]

So, the point (2, 9) lies on the line described by the equation \( y = 4x + 1 \). This method can be used to find any point on the line, making it a powerful tool for graphing and analysing linear relationships.