Question

write in point - slope form an equation of the line through the pair of points (1,0) and (10,15). type an equation of the line in point - slope form using one of the given points. (simplify your answer. use integers or fractions 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, $(x_1,y_1)=(1,0)$ and $(x_2,y_2)=(10,15)$. So $m=\frac{15 - 0}{10 - 1}=\frac{15}{9}=\frac{5}{3}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(1,0)$ and $m = \frac{5}{3}$, we get $y-0=\frac{5}{3}(x - 1)$.

Answer:

$y=\frac{5}{3}(x - 1)$