Question

How do you find the slope and $ y $ intercept for $ y = - 4x - 5? $

Answer 1

Hint: First we know that the slope-intercept form. Proportional linear functions can be written form $ y = mx + b $ , where $ m $ is the slope of the line. Non-proportional linear functions can be written in the form $ y = mx + b $ , $ b \ne 0 $ .
We find $ m $ and $ b $ .
After we use the Slope and Intercept form notations,
The notation is,
When $ b \ne 0 $ and $ m = 0 $ , the line is parallel to the $ x $ -axis and its equation is $ y = b $ .
Finally we get the slope and intercept for $ y $ .

Complete step-by-step solution:
The given equation is $ y = - 4x - 5 $ .This is the form of a line.
The slope-intercept form are
 $ y = mx + b $ , where $ m $ is the slope and $ b $ is the $ y $ intercept.
Find the values of $ m $ and $ b $ using the form
 $ y = mx + b $
We just get the value of $ m $ by compare the equation in general form
 $ m = - 4 $
Slope and Intercept form notations is,
When $ b \ne 0 $ and $ m = 0 $ , the line is parallel to the $ x $ -axis and its equation is $ y = b $ .
Since, we use the notation.
Here, $ b \ne 0 $
The $ y $ intercept is the value of $ b $
Then, $ y = - 5 $
The $ y $ intercept is the value is $ - 5 $

Note: Proportional linear functions can be written form $ y = mx + b $ , where $ m $ is the slope of the line. Non-proportional linear functions can be written in the form $ y = mx + b $ , $ b \ne 0 $ .This is called the slope-intercept form of a straight line because $ m $ is the slope $ b $ is the $ y $ -intercept.
The conditions are:
When $ b = 0 $ and $ m \ne 0 $ , the line passes through the origin and its equation is $ y = mx $ .
When $ b = 0 $ and $ m = 0 $ , the coincides with the $ x $ -axis and its equation is $ y = 0 $
When $ b \ne 0 $ and $ m = 0 $ , the line is parallel to the $ x $ -axis and its equation is $ y = b $ .