Question

How do I write $7x-y=3$ in slope-intercept form?

Answer 1

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$7x$.

& \Rightarrow 7x-y=3 \\\ & \Rightarrow 7x-y-7x=3-7x \\\ & \Rightarrow -y=3-7x \\\ \end{aligned}$$ Now we have the equation obtained is$$-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{aligned} & \Rightarrow -y=3-7x \\\ & \Rightarrow \dfrac{-y}{-1}=\dfrac{3-7x}{-1} \\\ \end{aligned}$$ Since we have divided both the sides by $$-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{aligned} & \Rightarrow \dfrac{-y}{-1}=\dfrac{3-7x}{-1} \\\ & \Rightarrow y=\dfrac{3-7x}{-1} \end{aligned}$$ Now, on the left hand side we get the variable y as singular. On the right hand side $$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{aligned} & \Rightarrow y=\dfrac{3-7x}{-1} \\\ & \Rightarrow y=\dfrac{3}{-1}-\dfrac{7x}{-1} \end{aligned}$$ Now we should divide 3 with $$-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{aligned} & \Rightarrow y=\dfrac{3}{-1}-\dfrac{7x}{-1} \\\ & \Rightarrow y=-3+7x \\\ & \Rightarrow y=7x-3 \end{aligned}$$ We compare this equation $$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.