Question

find the equation of the line that goes through the points (6, - 4) and (0, - 5)
what is the slope?
m=
what is the y - intercept?
y = mx + b
final answer
what is the equation of the line?

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(6,-4)$ and $(x_2,y_2)=(0,-5)$. Then $m=\frac{-5-(-4)}{0 - 6}=\frac{-5 + 4}{-6}=\frac{-1}{-6}=\frac{1}{6}$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. We know $m=\frac{1}{6}$ and we can use the point $(0,-5)$. Substituting $x = 0$, $y=-5$ and $m=\frac{1}{6}$ into $y=mx + b$, we get $-5=\frac{1}{6}\times0 + b$, so $b=-5$.

Step3: Write the equation of the line

Substitute $m=\frac{1}{6}$ and $b = - 5$ into $y=mx + b$. The equation of the line is $y=\frac{1}{6}x-5$.

Answer:

The slope $m=\frac{1}{6}$, the y - intercept $b=-5$, and the equation of the line is $y=\frac{1}{6}x - 5$