Question

How do you write an equation of a line with slope = $\dfrac{5}{2}$ and y-intercept ?

Answer 1

Hint: In order to solve this question, we use the slope-intercept formula. We are already given the value of the slope and the y-intercept, we simply place these values in the standard formula to find the equation of a line.
Standard form is given as $y = mx + c$

Complete step-by-step solution:
In this question, we are asked to find the equation of a line whose slope and y-intercept is given.
Slope refers to the angle formed by the given line with the positive side of the x-axis.
The slope is also known as the gradient. The intercept refers to the point at which the line cuts the axis.
On the x-axis, it will be known as x-intercept while on the y-axis, it will be known as y-intercept.
Now, the standard formula for finding any equation of a line is given as:
$y = mx + c$, where m= slope, y and x refer to the coordinates and c is the y-intercept.
The above formula is known as the slope intercept formula.
In this question, we are given the slope and c-intercept. Thus we simply substitute these values in the slope intercept formula.
Thus, $y = \dfrac{5}{3}x + 0$
$ \Rightarrow y = \dfrac{5}{3}x$

Therefore the standard equation of the line is $y = \dfrac{5}{3}x$.

Note: Some common properties of straight lines are:
A line which passes through origin makes zero intercept on the axes.
A horizontal line has no x-intercept and a vertical line has no y-intercept
The intercepts on the x-axis and y-axis are usually denoted by $a$ and $b$ respectively