Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as 2 comma 5 Expand Image Step 2: Choose another point on the line, such as 1 comma 3 Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is 1 half Step 4: Substitute those values into the point-slope form. y minus y sub 1 is equal to m times x minus x sub 1 y minus 3 is equal to 1 half times x minus 1 Which of Talia’s steps is incorrect?
Answer
A
Step 1 is incorrect because it uses a point that is not on the line.
B
Step 2 is incorrect because it uses a point that is not on the line.
C
Step 3 is incorrect because it shows an incorrect ratio for the slope.
D
Step 4 is incorrect because it shows an incorrect substitution of 1 comma 3 into the point-slope form.
Explanation
Slope is rise divided by run. Talia says the line rises 2 units and runs 1 unit to the right, so the slope is 2/1 = 2, not 1/2. The points she chose, (2, 5) and (1, 3), also give a slope of (5 − 3)/(2 − 1) = 2. Therefore, Step 3 is incorrect because it shows an incorrect ratio for the slope.
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