Question

write the equation of the line that passes through the given points (2,15) and (0, - 15). the equation of the line is . (simplify your answer. type your answer in slope - intercept form. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(2,15)$ and $(x_2,y_2)=(0, - 15)$. So, $m=\frac{-15 - 15}{0 - 2}=\frac{-30}{-2}=15$.

Step2: Find the y - intercept

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the line passes through the point $(0,-15)$. Substituting $x = 0$, $y=-15$ and $m = 15$ into $y=mx + b$, we get $-15=15\times0 + b$, so $b=-15$.

Step3: Write the equation of the line

Substitute $m = 15$ and $b=-15$ into $y=mx + b$. The equation of the line is $y = 15x-15$.

Answer:

$y = 15x-15$