Question

write the equation of this line in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

Let's take the points $(0, - 1)$ and $(1,6)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(x_1,y_1)=(0,-1)$ and $(x_2,y_2)=(1,6)$ gives $m=\frac{6-(-1)}{1 - 0}=\frac{6 + 1}{1}=7$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,-1)$, we have $b=-1$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m = 7$ and $b=-1$ gives $y=7x-1$.

Answer:

$y = 7x-1$