Question

How do you find the slope and intercept of $ y=3x-7 $ ?

Answer 1

Hint: Change of form of the given equation will give the slope and y intercept of the line $ y=3x-7 $ . We find the form of $ y=mx+k $ to find the slope m. Then, we get into the form of $ \dfrac{x}{p}+\dfrac{y}{q}=1 $ to find the intercepts of the line as p and q.

Complete step-by-step answer:
The given equation $ y=3x-7 $ is of the form $ y=mx+k $ . Here m is the slope of the equation of the line $ y=3x-7 $ .
This gives that the slope of the line $ y=3x-7 $ is 3.
Now we have to find the y intercept, and x-intercept of the same line $ y=3x-7 $ .
For this we convert the given equation into the form of $ \dfrac{x}{p}+\dfrac{y}{q}=1 $ . From the form we get that the x intercept, and y intercept of the line will be p and q respectively.
Simplifying the equation $ y=3x-7 $ , we get
 $
   y=3x-7 \\
  \Rightarrow 3x-y=7 \;
 $
The given equation is $ 3x-y=7 $ . Converting into the form of $ \dfrac{x}{p}+\dfrac{y}{q}=1 $ , we get
 $
   3x-y=7 \\
  \Rightarrow \dfrac{3x}{7}+\dfrac{y}{-7}=1 \\
  \Rightarrow \dfrac{x}{{}^{7}/{}_{3}}+\dfrac{y}{-7}=1 \;
 $
Therefore, the intercepts of the line $ 3x-y=7 $ is $ \dfrac{7}{3} $ and $ -7 $ .
The intercepting points for the line with the and X and Y-axis are $ \left( \dfrac{7}{3},0 \right) $ and $ \left( 0,-7 \right) $ .

Note: A line parallel to the 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. Same goes for lines parallel to the Y-axis. In case of slope of a line the range of the slope is 0 to $ \infty $ .