To write the equation of a line given the slope and the y-intercept, you can use the slope-intercept form of a linear equation, which is expressed as:
y = mx + b
In this formula:
- y represents the dependent variable (the output of the function),
- x is the independent variable (the input),
- m is the slope of the line, and
- b is the y-intercept, the point where the line crosses the y-axis.
For your specific case, the slope m is given as 1, and the y-intercept b is 4. Now, simply substitute these values into the equation:
y = 1x + 4
This can also be simplified to:
y = x + 4
Thus, the equation of the line with a slope of 1 and a y-intercept of 4 is y = x + 4. This equation represents a line that rises at a 45-degree angle since the slope of 1 indicates that for every unit increase in x, y increases by the same amount. Additionally, the line intersects the y-axis at the point (0, 4).