Question

How do you write an equation of line with slope:$\dfrac{3}{4}$, y-intercept:-5

Answer 1

Hint: The equation of a straight line in slope-intercept form is: $y = mx + b$. Where m is the value of slope and b is the y-intercept. Here, m and b are constants, and x and y are variables. Since x and y are variables that describe the position of specific points on the graph, m and b describe features of the function. A straight line is a linear equation of the first order. Substitute the values of m and b in the line equation.

Complete step-by-step answer:
Here, we want to construct a linear equation of the line.
The slope is $\dfrac{3}{4}$ and the y-intercept is -5.
As we already know the line equation.
The line equation is $y = mx + b$.
Here, the value of m is $\dfrac{3}{4}$ and the value of b is -5.
 Let us substitute the values of m and b.
Therefore,
$ \Rightarrow y = \dfrac{3}{4}x + \left( { - 5} \right)$
Now, simplify the above equation.

$ \Rightarrow y = \dfrac{3}{4}x - 5$
Finally, we get the equation of a straight-line.

Note:
Slope: The slope of a line is the ratio of change in y over the change in x between any two points on the line.
$slope\left( m \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Positive slope: It means that two variables are positively related; that is, when x increases, so do y, and when x decreases, y decreases also. The line with the positive slope on the line graph moves from left to right and the line rises.
Negative slope: A negative slope means that two variables are negatively related; that is, when x increases, y decreases, and when x decreases, y increases. The line with the negative slope on the line graph moves from left to right and the line falls.
The slope is a horizontal line then the value of y is always the same.
The slope is a vertical line then the value of x is always the same.