Question

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

Answer 1

Hint: Since, we already have the equation in the slope-intercept form, we will compare it with $ y = mx + c $ to find the value of $ m $ as it represents as the slope of the line. Then, as we know that there are two kinds of intercepts which are $ x $ -intercept and $ y $ -intercept. So, $ x $ -intercept is the point where the line intersects the $ x $ -axis and $ y $ -intercept is the point where the line intersects the $ y $ -axis. So, to calculate the intercepts, we will put $ x $ and $ y $ as zero one by one.

Complete step-by-step answer:
(i)
We are given the line equation:
 $ y = - 5x - 4 $
Now, since we have our equation in the slope-intercept form, we will compare the above equation with $ y = mx + c $ to find the value of $ m $ .
As we can see that the coefficient of $ x $ is $ m $ , in our equation the coefficient of $ x $ is $ - 5 $ .
i.e.,
 $ m = - 5 $
Therefore, the slope of the equation $ y = - 5x - 4 $ is $ - 5 $
(ii)
Now, as we know that $ x $ -intercept is the point where the line crosses the $ x $ -axis and we also know that on $ x $ -axis, $ y = 0 $ . Therefore, to find the $ x $ -intercept, we will put $ y $ as $ 0 $ in the equation of line given to us. Therefore,
 $
  0 = - 5x - 4 \\
  5x = - 4 \\
  x = - \dfrac{4}{5} \;
  $
Therefore, the $ x $ -intercept of the equation $ y = - 5x - 4 $ is $ - \dfrac{4}{5} $ .
(iii)
Similar to $ x $ -intercept, $ y $ -intercept is the point where the line crosses the $ y $ -axis and we also know that on $ y $ -axis, $ x $ =0. Therefore, to find $ y $ -intercept, we will put $ x $ as $ 0 $ in the equation of the line given to us. Therefore,
 $
  y = - 5\left( 0 \right) - 4 \\
  y = - 4 \;
  $
Therefore, the $ y $ -intercept of the equation $ y = - 5x - 4 $ is $ - 4 $ .

Note: A line parallel to $ x $ -axis, does not intersect the $ x $ -axis at any finite distance and hence, we cannot get any finite $ x $ -intercept of such a line. Slope of such a line is $ 0 $ . Similarly, lines parallel to the $ y $ -axis, do not intersect $ y $ -axis at any finite distance and hence, we cannot get any finite $ y $ -intercept of such a line. Slope of such a line is $ \infty $ .
In an equation of the form $ y = mx + c $ , $ m $ represents the slope of the line and $ c $ represents the vertical intercept or $ y $ -intercept of the line as it is the value of $ y $ when $ x = 0 $ . Also, there is an alternative method to find the intercepts of a line equation. Convert the given line equation into intercept form of a line i.e., $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ , where $ a $ is the $ x $ -intercept and $ b $ is the $ y $ -intercept.