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.