Question

How do I write \[7x-y=3\] in slope-intercept form?

Answer 1

Hint: If we want to convert the equation in slope intercept form it should be written as\[y=mx+c\]. Here\[m\]is the slope, and \[c\]is the intercept on the y-axis. We can find the slope of the line very easily using this formula.

Complete step by step solution:
To convert the equation of the line \[7x-y=3\] into the slope and intercept form subtract both sides with\[7x\].
\[\begin{align}
  & \Rightarrow 7x-y=3 \\
 & \Rightarrow 7x-y-7x=3-7x \\
 & \Rightarrow -y=3-7x \\
\end{align}\]
Now we have the equation obtained is\[-y=3-7x\]. If we convert this new equation into the slope-intercept form, first of all we divide both that sides by $-1$.
\[\begin{align}
  & \Rightarrow -y=3-7x \\
 & \Rightarrow \dfrac{-y}{-1}=\dfrac{3-7x}{-1} \\
\end{align}\]
Since we have divided both the sides by \[-4\] the equation looks like \[\dfrac{-y}{-1}=\dfrac{3-7x}{-1}\]. On the left hand side the number \[-1\] in the numerator cancels the number \[-4\] in the denominator.
The equation now looks like this:
\[\begin{align}
  & \Rightarrow \dfrac{-y}{-1}=\dfrac{3-7x}{-1} \\
 & \Rightarrow y=\dfrac{3-7x}{-1}
\end{align}\]
Now, on the left hand side we get the variable y as singular. On the right hand side \[3-7x\] is divided by \[-1\]. Derive 2 individual fractions from the fraction \[\dfrac{3-7x}{-1}\]. To do this we divide 3 by \[-1\] and then add the subtraction sign and then divide $7x$ by \[-1\].
The equation now looks like this:
\[\begin{align}
  & \Rightarrow y=\dfrac{3-7x}{-1} \\
 & \Rightarrow y=\dfrac{3}{-1}-\dfrac{7x}{-1}
\end{align}\]
Now we should divide 3 with \[-1\] to get \[-3\]. The negative sign from \[-1\] will form a positive sign it gets multiplied with negative sign in subtraction sign from positive sign.
The equation now looks like:
\[\begin{align}
  & \Rightarrow y=\dfrac{3}{-1}-\dfrac{7x}{-1} \\
 & \Rightarrow y=-3+7x \\
 & \Rightarrow y=7x-3
\end{align}\]
We compare this equation \[y=7x-3\] with the equation in slope and intercept form i.e.\[y=mx+c\]. We have got the slope-intercept form of the equation.

Note:
Always convert the equation into slope-intercept form i.e. \[y=mx+c\] or linear expression in one variable and make sure that coefficient of \[y\] is always 1 and \[c\] is a constant.