Question

How do you find the slope and intercept of $3x+4y=7$ ?

Answer 1

We have been given the equation of a straight-line which is in the standard form. In order to find the slope and intercept of the line, we must first convert it into the slope-intercept form. Therefore, we must have proper knowledge of the various forms of the equation of straight-line including the standard form and the slope-intercept form.

Complete step-by-step solution:
The standard form of a line is given as:
$ax+by+c=0$
Where,
$a=$ coefficient of x-variable
$b=$ coefficient of y-variable
$c=$ constant term
We can put various values of x or y-variable to find any particular point on line. If we input the value of both the x and y-component of the point, we can also verify whether that point lies on that particular line or not.
The slope-intercept form of a line is expressed as:
$y=mx+c$
Where,
$m=$ slope of line
$c=$ intercept of the line
We shall make changes to the given equation, $3x+4y=7$accordingly.
The term with y-variable is on the right-hand side of the equation and the constant term is on the left-hand side of the equation, thus we shall take the term with x-variable on the right-hand side of the equation.
$\Rightarrow 4y=-3x+7$
We will now divide the whole equation by 4 to make the coefficient of y equal to 1:
$\Rightarrow \dfrac{4y}{4}=\dfrac{-3x}{4}+\dfrac{7}{4}$
$\Rightarrow y=-\dfrac{3}{4}x+\dfrac{7}{4}$
Hence, the equation, $3x+4y=7$ changes into its slope-intercept form as $y=-\dfrac{3}{4}x+\dfrac{7}{4}$.
Therefore, the slope of the equation is $-\dfrac{3}{4}$ and the intercept is $\dfrac{7}{4}$.

Note: One thing to be taken care of is that the coefficient of y-variable is always 1 in the slope-intercept form of a straight line. Therefore, we must divide the entire equation with the coefficient of y to make it equal to one. If we do not make the coefficient of y equal to 1, then we might even end up getting incorrect slope and intercept of line.