We have to find the equation of the red line
To get the equation of the line in the slope-intercept form,
we need its slope and its y-intercept
Finding the Slope
we know that the slope of a line is the rise of the line / run of the line between 2 points
here, the 2 points are already marked on the graph
So, slope = rise / run
we notice that the line rises only 2 units and runs 8 units between the points: (-5 , 3 ) and (3 , 5)
Slope = rise / run
now that we know the values of rise and run, we can plug the values to get the slope
Slope = 2 / 8
Slope = 1 / 4
Finding the y-intercept
We will now look at the point (-5 , 3) , we know that the slope is 1/4.
which means that every time the line moves 1 unit to the right, it also moves 1/4 units up
So, until the point (-1 , 4), the line has finally ascended 1 unit and now is at a proper coordinate
We can see that the line is only 1 unit to the left of the y-axis, so the y-coordinate of the line after moving 1 unit to the right is the y-intercept
since the line ascends 1/4 units every time it moves 1 unit to the right,
the ordinate of the line at the y-axis will be 1/4 more than the last ordinate (which was 4)
y-intercept = (4 + 1/4)
y-intercept = 17 / 4
Equation of the line
From the question, we know that the general form of the slope-intercept form is :
y = mx + b (where m is the slope and b is the y-intercept)
y = (1/4)x + (14/4)
y = (x + 14) / 4
