Question

What is the equation in point−slope form of the line passing through (1, 2) and (2, 5)?

(y − 2) = −3(x − 1)

(y − 2) = 3(x − 1)

(y − 1) = −3(x − 2)

(y + 2) = 3(x + 1)

Answer 1

@Zepdrix

Answer 2

\[\large\rm (y-\color{cornflowerblue}{y_1})=\color{orangered}{m}(x-\color{cornflowerblue}{x_1})\]For point-slope, we'll need a point and a slope value.
They've already provided points for us.
We just have to do the work and find the correct slope (rate of change) value.

Answer 3

\[\large\rm \color{orangered}{m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{2-1}}\]

Answer 4

\[\large\rm \color{orangered}{m=3}\]So there is our slope value.\[\large\rm (y-\color{cornflowerblue}{y_1})=\color{orangered}{3}(x-\color{cornflowerblue}{x_1})\]
Then we need to plug in whichever point will match one of our options.

Answer 5

If we plug in the point (1,2),\[\large\rm (y-\color{cornflowerblue}{2})=\color{orangered}{3}(x-\color{cornflowerblue}{1})\]
it looks that is one of our options.

Answer 6

yes

Answer 7

wow thank you