Question

Graph the line y= 1/3x+6

Answer 1

Graph of
`\(y = (1)/(3)x + 6\)` has a slope of
`\((1)/(3)\)`, y-intercept at (0, 6), and a positive trend.

The given equation is in slope-intercept form,
`\(y = (1)/(3)x + 6\)`, where the coefficient of \(x\) represents the slope and the constant term is the y-intercept. In this case, the slope is
`\((1)/(3)\)`, indicating that for every one unit increase in x, the corresponding y value increases by
`\((1)/(3)\)`.

The y-intercept is 6, which means the line intersects the y-axis at the point (0, 6). To graph the line, start by plotting this point. From there, use the slope to find another point, such as moving one unit to the right and three units up (rise over run). Connect the two points with a straight line.

The line has a positive slope, indicating a rising trend from left to right. As x increases, y increases at a slower rate due to the fraction
`\((1)/(3)\),` making the line less steep than a line with a slope of 1.

The graph represents a linear relationship between x and y, forming a straight line on the coordinate plane. The slope and y-intercept provide insights into the behavior of the line as it extends infinitely in both directions.