Question

How do you write an equation of a line given no slope, $\left( { - 3,\dfrac{3}{4}} \right)$?

Answer 1

Hint: To solve the given question follow up the given step-by-step method to find an accurate solution. Slope is calculated by finding the ratio of the “vertical change” to the “horizontal change” between two distinct points on a line. Sometimes the ratio is expressed as a quotient, giving the same number for every two distinct points on the same line.

Complete step-by-step solution:
If no slope is given, we can let the slope = $m$
Given the point we can use the point-slope formula to write the equation for this problem. The point-slope formula states: $\left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right)$
Where $m$is the slope and $\left( {{x_1}{y_1}} \right)$ is a point the line passes through.
Substituting the values from the point in the problem and letting the slope equal $m$the equation is:
$
  \left( {y - \dfrac{3}{4}} \right) = m\left( {x - \left( { - 3} \right)} \right) \\
  \left( {y - \dfrac{3}{4}} \right) = m\left( {x + 3} \right) \\
 $

Additional Information: In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter; there is no clear answer to the question why the letter $m$is used for slope, but its earliest use in English appears in O’Brien who wrote the equation of a straight line as “ $y = mx + b$” and it can also be found in Todhunter who wrote it as .

Note: The following mentioned are a few tips to solve the given question and other similar questions.
i) A line is increasing if it goes up from left to right. The slope is positive, i.e., $m > 0$
ii) A line is decreasing if it goes down from left to right. The slope is negative, i.e., $m < 0$
iii) If a line is vertical the slope is zero. This is a constant function.
iv) If a line is vertical the slope is undefined.