Method Used:
We will use the point-slope equation to find the slope of this line
We know that according to the point-slope equation:
y = mx + b (where m is the slope and b is the y-intercept of the line)
Now, we will find the slope and the y-intercept of the line in order to find the equation of this line
Finding the Equation:
Finding the Slope:
We know that the formula for finding the slope of a line is:
Slope = Rise / Run
We will check the slope between the points, (-9,0) and (-6,2)
We know that rise = y2 - y1 (y of the second - y of the first coordinate)
Rise = 2 - 0 (replacing the values)
Rise = 2
We know that Run = x2 - x2 (x of the second - x of the first coordinate)
Run = -6 - (-9) (replacing the values)
Run = 3
Now that we know the values of Rise and Run, we can find the slope
Slope = Rise / Run
Slope = 2 / 3
Finding the Y-intercept:
We know that the y-intercept of a line is the y-coordinate of the point where the line intersects the y-axis
We can see in the graph that the line intersects the y-axis at the point (0,6)
the y-coordinate of the point (0,6) is 6
Therefore, the line has a y-intercept of 6
Equation of the Line:
We know that the general form for the slope-intercept formula is:
y = mx + b (where m is the slope and b is the y-intercept)
replacing the values of slope and y-intercept
y = (2/3)x + 6
Therefore, the equation of the line in the Graph is y = (2/3)x + 6