Question

How do you find the slope of \[\left( 6,3 \right),\left( 7,-4 \right)\] ?

Answer 1

Hint: In this problem, we have to find the value of the slope from the given two points. We should know that the slope or gradient of a line describes its steepness, incline or grade. We know that for finding slope, we have different formulas based on the given problem. In this problem, we are given two points for the slope to be found. We can use two points to find the slope with the given points.

Complete step by step answer:
We know that, to find the value of slope we can use two points form.
Two points form a slope is the ratio of coordinate of first point in the line to the coordinates of second point in the line. i.e.,
\[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
We know that the given two points to find the slope is,
Point 1 = \[\left( 6,3 \right)\],
\[{{x}_{1}}=6,{{y}_{1}}=3\]
Point 2 = \[\left( 7,-4 \right)\].
\[{{x}_{2}}=7,{{y}_{2}}=-4\].
We can substitute the above values in the two points formula to find the slope, we get
\[\begin{align}
  & \Rightarrow m=\dfrac{-4-3}{7-6} \\
 & \Rightarrow m=-7 \\
\end{align}\]
Therefore, the value slope from the given two points \[\left( 6,3 \right),\left( 7,-4 \right)\]is -7.

Note:
Students make mistakes in choosing an appropriate formula for the given problem, which should be concentrated. We should know some basic slope formulas to solve these types of problems. We should know that the slope or gradient of a line describes its steepness, incline or grade. If we are given an angle, we have another formula to find the slope value.