Question

write the point - slope form of the line satisfying the given conditions. then use the point - slope form of the equation to write the slope - intercept form of the equation
passing through (6,12) and (9,18)

type the point - slope form of the equation of the line
(simplify your answer. use integers or fractions for any number in the equation.)

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(6,12)$ and $(x_2,y_2)=(9,18)$:
$m = \frac{18 - 12}{9 - 6} = \frac{6}{3} = 2$

Step2: Write point-slope form

Point-slope form is $y - y_1 = m(x - x_1)$. Use $(6,12)$ and $m=2$:
$y - 12 = 2(x - 6)$
(Note: Using $(9,18)$ would give $y - 18 = 2(x - 9)$, which is also valid)

Step3: Convert to slope-intercept form

Expand and solve for $y$:
$y - 12 = 2x - 12$
$y = 2x - 12 + 12$
$y = 2x$

Answer:

Point-slope form:

$y - 12 = 2(x - 6)$ (or equivalent $y - 18 = 2(x - 9)$)

Slope-intercept form:

$y = 2x$