a line passes through the points (-2, -16) and (5, 19). write its equation in slope - intercept form. write…

a line passes through the points (-2, -16) and (5, 19). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

a line passes through the points (-2, -16) and (5, 19). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-2,-16)$ and $(x_2,y_2)=(5,19)$. Then $m=\frac{19-(-16)}{5 - (-2)}=\frac{19 + 16}{5+2}=\frac{35}{7}=5$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(-2,-16)$ and $m = 5$. So $y-(-16)=5(x - (-2))$, which simplifies to $y + 16=5(x + 2)$. Expand the right side: $y+16 = 5x+10$. Solve for $y$: $y=5x+10 - 16$, so $y=5x - 6$.

Answer:

$y = 5x-6$