The line with a y-intercept of 1/4 and a slope of 1/4 intersects the y-axis at (0, 1/4) and rises gently, increasing by 1/4 for every unit moved to the right. The graph forms a diagonal line on the coordinate plane, depicting the relationship between x and y.
The equation of a line can be expressed in the slope-intercept form (y = mx + b), where (m) is the slope and (b) is the y-intercept. In this case, the line has a y-intercept of 1/4 and a slope of 1/4.
The y-intercept, denoted as (b), is the point where the line intersects the y-axis. For this line, it occurs at the point (0, 1/4). This means that when (x) is zero, (y) is 1/4.
The slope, denoted as (m), represents the rate at which the line changes in the vertical direction for a unit change in the horizontal direction. A slope of 1/4 implies that for every increase of 1 unit in (x), (y) increases by 1/4.
To graph this line, start at the y-intercept (0, 1/4) and use the slope to find another point, such as moving 4 units to the right and 1 unit up. Connect these points, and you have a straight line. The line will rise gently, indicating a positive slope, and pass through the y-axis at the y-intercept.
In summary, the line with a y-intercept of 1/4 and a slope of 1/4 rises gradually as you move to the right, forming a diagonal line on the coordinate plane.