Question

find the equation of the line that passes through the points (-5,0) and (1,-6). give the equation in the form y = mx + b. y = question help: message instructor submit question jump to answer

Explanation:

Step1: Calculate the slope \( m \)

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1,y_1)=(-5,0) \) and \( (x_2,y_2)=(1,-6) \). So, \( m=\frac{-6 - 0}{1 - (-5)}=\frac{-6}{6}=-1 \).

Step2: Find the y - intercept \( b \)

We use the point - slope form \( y - y_1=m(x - x_1) \) and then convert it to \( y=mx + b \). We can use the point \( (-5,0) \) and \( m=-1 \). Substitute into \( y - y_1=m(x - x_1) \): \( y - 0=-1(x - (-5)) \), which simplifies to \( y=-x - 5 \). We can also check with the other point \( (1,-6) \). Substitute \( x = 1 \) and \( y=-6 \) into \( y=mx + b \), we have \( -6=-1\times1 + b \), so \( -6=-1 + b \), and \( b=-6 + 1=-5 \).

Answer:

\( y=-x - 5 \)