Error: Slope formula used incorrectly. Correct Solution: y=- 3/5x+4
Practice makes perfect
First we will solve the problem ourselves. Then we will compare our solution with the incorrect one to identify the error. Let's do it!
Finding the Slope
We want to write the equation of the graph in slope-intercept form.
y= mx+ bWe find the slope m of a line by dividing the vertical change by the horizontal change between two points on the line. We can use the Slope Formula for this purpose.
Slope=y_2-y_1/x_2-x_1
The two points on the line are given as ( 0, 4) and ( 5, 1). Let's substitute these into the above formula and simplify.
Now we have found that the slope is - 35. The y-intercept b is the point where the graph intercepts the y-axis. That point is marked on the graph.
Knowing that the y-intercept is 4, we can write the equation for the line.
y= - 35x+ 4
Comparing Solutions
We see that the slopes are different. Our negative slope must be correct, because the line is sloping downward. The mistake made in the shown solution was in calculating the slope. When using the Slope Formula the coordinates must be written into the formula in the correct order.
