Question

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, 5).
Step 2: Choose another point on the line, such as (1, 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 .
Step 4: Substitute those values into the point-slope form.

y – y1 = m(x – x1)

y – 3 = (x – 1)

Which of Talia’s steps is incorrect?

Step 1 is incorrect because it uses a point that is not on the line.
Step 2 is incorrect because it uses a point that is not on the line.
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.

Answer 1

The slope is incorrect in the equation.
Step 3 was the calculation of the slope.

Answer 2

Step 3 is incorrect because it shows an incorrect ratio for the slope.

Explanation:

By the given diagram,

The points (1,3) and (2,5) lie on the line,

⇒ Steps 1 and 2 are correct.

Now, the slope of the line will be the ratio of rise and run from (1,3) and (2,5),

Rise = 2 units up,

Run = 1 unit right,

Thus, the slope of the given line is , m = 2,

Now, the slope intercept form of a line is,

`y-y_1=m(x-x_1)`

Where,
`(x_1,y_1)` is any point on the line,

Here,
`x_1=1`
`y_1=3`

Thus, the equation of the given line would be,

`y-3=2(x-1)`

So, he put (1,3) correctly in the formula.

Hence, it is clear that he made his mistake on step 3rd.

Step 3 is the incorrect step.