Answer:
Step completed incorrectly: 2
Correct Answer: y = -4x + 22
Step-by-step explanation:
The graph is a straight line through points M(4, -1) and N(8, 0). Point Q is located at (6, -2).
To calculate the slope of the line, substitute the points into the slope formula:
[tex]\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}[/tex]
Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.
If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.
The negative reciprocal of 1/4 is -4.
Therefore, the slope of the perpendicular line is -4.
So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.
Corrected work
[tex]\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}[/tex]
[tex]\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4[/tex]
[tex]\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}[/tex]
[tex]\textsf{Step 4:} \quad y+2=-4x+24[/tex]
[tex]\textsf{Step 5:} \quad y+2-2=-4x+24-2[/tex]
[tex]\textsf{Step 6:} \quad y=-4x+22[/tex]
Therefore, step 2 has been completed incorrectly.
The correct answer is y = -4x + 22.
