Question

what is the equation in point-slope form of the line passing through (0,6) and (1,3)

Answer 1

Answer:

$y = -3x+6$

Step-by-step explanation:

Coordinates are (0,6) and (1,3)

Slope = $\frac{rise}{run}$

Slope = $\frac{3-6}{1-0}$

Slope = -3

Now, Finding b

Taking any Point

Point = (x,y) = (0,6)

So, x = 0, y = 6

Putting in slope-intercept form to find b

$y =mx+b$

=> 6 = (-3)(0)+b

=> b = 6

Now Putting slope and b in the formula to get the required slope-intercept form.

$y =mx+b$

=> $y = -3x+6$

Answer 2

Answer: $y - 3 = -3(x - 1)$

Step-by-step explanation:

You can start by finding the slope (m), $\frac{y1 - y2}{x1 - x2}$:

$\frac{y1 - y2}{x1 - x2} = \frac{6 - 3}{0 - 1} = \frac{3}{-1} = -3.$

Now, plug the range and one points into the point-slope form equation, $y - y1 = m(x - x1)$:

$y - y1 = m(x - x1)$

$y - 3 = -3(x - 1)$