Question

Write and equation in slope-intercept form for the line that passes though (3,1) and (1,2)

Answer 1

Answer: Choice C
`\text{y} = -(1)/(2)\text{x}+(5)/(2)`

Step-by-step explanation

We'll need to compute the slope first.

`\text{Given Points: }(x_1,y_1) = (3,1) \text{ and } (x_2,y_2) = (1,2)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (2 - 1)/(1 - 3)\\\\m = (1)/(-2)\\\\m = -(1)/(2)\\\\`

The slope is -1/2.

It means "down 1, right 2" because rise = -1 and run = 2.

Then we'll apply point-slope form to get the following steps.

`\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-1 = -(1)/(2)(\text{x}-3)\\\\\text{y}-1 = -(1)/(2)\text{x}-(1)/(2)(-3)\\\\\text{y}-1 = -(1)/(2)\text{x}+(3)/(2)\\\\`

`\text{y}-1+1 = -(1)/(2)\text{x}+(3)/(2)+1\\\\\text{y} = -(1)/(2)\text{x}+(3)/(2)+1\\\\\text{y} = -(1)/(2)\text{x}+(3)/(2)+(2)/(2)\\\\\text{y} = -(1)/(2)\text{x}+(3+2)/(2)\\\\\text{y} = -(1)/(2)\text{x}+(5)/(2)\\\\`

The equation is in slope intercept form y = mx+b

m = -1/2 = slope

b = 5/2 = y intercept

Therefore the answer is choice C

To verify this answer, plug in x = 3 to find that it leads to y = 1.

Also, x = 1 should lead to y = 2. I'll let the student do each of these calculations.

Another way to verify the answer is to use a graphing tool like Desmos or GeoGebra. The two points (3,1) and (1,2) should both be on the line.

Side notes

• -1/2 = -0.5
• 3/2 = 1.5
• 5/2 = 2.5