Question

How do you write $5x-y=\dfrac{1}{4}$ into slope intercept form?

Answer 1

In this question, we have to find the slope intercept form of the equation. Thus, we will find the slope and intercept and then use slope-intercept form to get the solution. First, we will transform the equation into the general line of the equation $y=mx+c$ , by subtracting 5x on both sides and then multiply (-1) on both sides of the equation, to get the transformed equation. Thus, we compare the general line of the equation and transformed equation, to get the value of slope and intercepts of the equation, to get the required answer

Complete step by step answer:
In this question, we have to solve the equation $5x-y=\dfrac{1}{4}$ to get the slope-intercept form.
As we know, the equation of the line is equal to $y=mx+c$ , where m is the slope of the equation = $\dfrac{y}{x}=\dfrac{\text{rise}}{\text{run}}$ , means y will go vertically and x will go horizontal. In addition, c is the y-intercept =constant ------------- (1)
Therefore, we rearrange the equation $5x-y=\dfrac{1}{4}$ in the form of $y=mx+c$ , that is
Now, we will subtract 5x on both sides of the above equation, we get
$\Rightarrow 5x-y-5x=\dfrac{1}{4}-5x$
As we know, the same terms with opposite signs will cancel out, we get
$\Rightarrow -y=\dfrac{1}{4}-5x$
Now, we will multiply (-1) on both sides in the above equation, we get
$\Rightarrow -y\times \left( -1 \right)=\left( \dfrac{1}{4}-5x \right)\times \left( -1 \right)$
Therefore, we get
$\Rightarrow y=5x-\dfrac{1}{4}$
As we see the above equation has transformed into the equation $y=mx+c$ , thus $m=5$ , and $c=-\dfrac{1}{4}$ .
Thus, for the equation $5x-y=\dfrac{1}{4}$ ,its slope-intercept form is equal to $y=5x-\dfrac{1}{4}$ .

Note:
Always do step-by-step calculations to get the exact slope and intercept of the equation. Always mention the slope-intercept form and its formula, to get an accurate solution.