Question

The slope of the line is 5 and passing through (9, 8). Find its equation.

Answer 1

Hint: If any line has slope as m, and it passes through the point $\left( {{x_1},{y_1}} \right)$ then the equation of the line can be expressed as $(y - {y_1}) = m(x - {x_1}).$

Complete step-by-step answer:
Given that the slope of the line is, m=5 and passing through point $\left( {{x_1},{y_1}} \right)$ = (9, 8).
Using the equation of line which is given by
\[ \Rightarrow (y - {y_1}) = m(x - {x_1})\]
Substituting the values of slope and point in the above equation we get
\[
   \Rightarrow (y - 8) = 5 \times (x - 9) \\
   \Rightarrow y - 8 = 5x - 45 \\
   \Rightarrow y = 5x - 37 \\
  \]
Hence, the equation of line is given by \[y = 5x - 37\]

Note: To solve these types of questions remember the equations of all forms of straight lines such as slope intercept form. Also the slope of a line refers to the ratio of the vertical change in y over the horizontal change in x between any two points on a line. If the slope is positive, the line slants upward to the right. If the slope is negative, the line slants downward to the right.