Question

hw 1 - algebra for calculus section 0.1: problem 4 (1 point) find an equation of the line passing through the points (-2, -4) and (-7, -39).

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, $x_1=-2,y_1 = - 4,x_2=-7,y_2=-39$. So $m=\frac{-39-(-4)}{-7-(-2)}=\frac{-39 + 4}{-7 + 2}=\frac{-35}{-5}=7$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-2,-4)$ and $m = 7$, we have $y-(-4)=7(x-(-2))$.

Step3: Simplify the equation

$y + 4=7(x + 2)$; expand the right - hand side: $y+4=7x + 14$; then subtract 4 from both sides to get the slope - intercept form $y=7x+10$.

Answer:

$y = 7x+10$