Question

How do you rewrite the equation $2y + 3x = 4$ in slope intercept form?

Answer 1

As we know that the given equation is a linear equation in two variables. An equation of the form $px + qy = r$ , where $p,q$ and $r$ are real numbers and the variables $p$ and $q$ are not equivalent to zero, is called linear equation in two variables. The slope intercept form of a linear equation has the following term where the equation is solved for $y$ in terms of $x:y = a + bx$ , $b$ is the slope and $a$ is a constant term.

Complete step by step solution:
We will rewrite the standard form of the linear equation: $ax + by = c$ $\Rightarrow 3x + 2y = 4$ . The slope intercept form of the equation is $y = mx + b$ .
We convert the standard form to slope-intercept form, solve for y. $3x + 2y = 4$ .
Subtract $3x$ from both sides, $2y = - 3x + 4$ . Now we will divide both the sides by $2$ .
$y = - \dfrac{3}{2}x + \dfrac{4}{2}$ , On further simplifying we get $\Rightarrow y = - \dfrac{3}{2}x + 2$ .

Hence the slope intercept form of the above equation is $y = - \dfrac{3}{2}x + 2$ .

Note: We know that the formula of slope intercept form is $y = mx + b$ where $y$ is the “y” coordinate, $m$ is the slope, $x$ is the “x” coordinate and $b$ is the ‘y’ intercept. We can use this form of linear equation to draw the graph of the given equation on the “x” and “y” coordinate plane. We should keep in mind that the conversion of the equation of the line to slope intercept form is done by simple manipulation. $Y$ intercept of the line is the point where the line cuts the ‘y’ axis and the slope is tan of the angle that is made by the line on the x- axis.