Answer :
Answer:
The line will have a positive slope.
Step-by-step explanation:
Slope
Slope is the rate of change in the y-axis over the x-axis. Slope is also synonymous with "rise over run" where "rise" is the change in y and "run" is the change in x.
The formula for slope, given two points, is,
[tex]\dfrac{rise}{run} =\dfrac{\Delta y}{\Delta x} =\dfrac{y_2-y_1}{x_2-x_1}[/tex] ,
where the subscripts 1 and 2 indicate from which coordinate pair it originates from.
Applying the Formula
We're given the x and y intercepts of a line, which are apart of the line. So, to calculate the line's slope we can plug their coordinate pair values into the formula.
Let the y-intercept [tex](0,5)=(x_2,y_2)[/tex] and the x-intercept [tex](-6,0)=(x_1,y_1)[/tex].
[tex]slope=\dfrac{5-0}{0-(-6)} =\dfrac{5}{6}[/tex]
The slope of the line is a positive value, thus it has a positive slope!
Solution 2: Intuition
The x-intercept is located to the left of the origin and the y-intercept is directly above. Visualizing it, the y-intercept is to the right and up relative to the x-intercept
Since the value of the x-coordinate of the y-intercept is greater, we can conclude that as x gets bigger so does its y-value; this feature is unique to a positive slope.
