Question

How do you write $5x-y=1$ 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. As we know that, the slope is the ratio of the vertical change or horizontal change between any two distinct points on the curve. About intercepts, the x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. Thus, we transform the equation into the line of the equation $y=mx+c$ , by adding 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, which is our required answer

Complete step by step answer:
In this question, we have to solve the equation $5x-y=1$ using 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 $5x-y=1$ in the form of $y=mx+c$ , that is
The equation given to us is $5x-y=1$---------- (2)
Now, we will subtract 5x on both sides of the equation (2), we get
$\Rightarrow 5x-y-5x=1-5x$
As we know, the same terms with opposite signs will cancel out, we get
$\Rightarrow -y=1-5x$
Now, we will multiply (-1) on both sides in the above equation, we get
$\Rightarrow -y\times \left( -1 \right)=\left( 1-5x \right)\times \left( -1 \right)$
Therefore, we get
$\Rightarrow y=5x-1$ ---------- (3)
As we see the above equation has transformed into the equation $y=mx+c$ .
Therefore, on comparing equations (1) and (3), we get that
The slope of the equation $5x-y=1$ = $m=5$ , and
The intercept of y-axis $5x-y=1$ = $c=-1$ .
Thus, for the equation $5x-y=1$ , its slope-intercept form is equal to $y=5x-1$ .

Note:
Always do proper calculations to get the exact slope and intercept of the equation. You can also find the y-intercept by using the substitution method. Let x=0 in the equation and solve for y, which is the required y-intercept for the answer. Then, put the value in the general form of the equation, to get the required solution.