Question

How to find the slope of a line with one number given \[y = 1.5\] or \[x = - 7\]?

Answer 1

Hint: Here in this question, we have to find the slope of a line of given and y and x intercepts. Firstly, we have to find the points \[\left( {{x_1},{y_1}} \right)\] and \[\left( {{x_2},{y_2}} \right)\] using intercepts. Find the slope by rearranging the Point-Slope formula \[y - {y_1} = m\left( {x - {x_1}} \right)\] as \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]. On simplification to the point-slope formula we get the required solution.

Complete step-by-step answer:
Consider the given 1.5 was the y-intercept i.e., \[y = 1.5\] and -7 was the x-intercept i.e., \[x = - 7\]
These two intercepts would give us two points \[\left( {0,1.5} \right)\] and \[\left( { - 7,0} \right)\].
Now we have to find the slope of the line passing through the points \[\left( {0,1.5} \right)\] and \[\left( { - 7,0} \right)\].
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Consider, the point-slope formula
\[y - {y_1} = m\left( {x - {x_1}} \right)\]-------(1)
The point-slope formula uses the slope and the coordinates of a point along the line to find the y-intercept.
Find the slope \[m\]in point-slope formula by using the formula \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
Where \[{x_1} = 0\], \[{x_2} = - 7\], \[{y_1} = 1.5\] and \[{y_2} = 0\] on substituting this in formula, then
 \[ \Rightarrow m = \dfrac{{0 - 1.5}}{{ - 7 - 0}}\]
\[ \Rightarrow m = \dfrac{{ - 1.5}}{{ - 7}}\]
On simplification, we get
\[ \Rightarrow m = 0.2143\]
Hence, the gradient or slope of the line passing through points \[\left( {0,1.5} \right)\] and \[\left( { - 7,0} \right)\] or the intercepts \[y = 1.5\] or \[x = - 7\] is \[m = 0.2143\].
So, the correct answer is “\[m = 0.2143\]”.

Note: The slope of a line is a ratio of the change in the y value and the change in the x value. We have to know the equation of a line and then we have to substitute the values to the equation, hence we can determine the value. While simplifying the equation we must take care of signs of terms.