Question

What is the slope – intercept form of $3x + 2y = 2?$

Answer 1

Hint: The equation of a line in slope- intercept form is $y = mx + b$ where $m$ is the slope is and $b$ is the $y$-intercept. Arrange the given equation in the form of slope- intercept. Using the slope –intercept formula rearrange the given equation as the form of slope.
Formula used:
Slope-intercept form,
$y = mx + b$
$y = y$ Coordinate
$m = $ Slope
$x = x - $ Coordinate
$b = y$ Intercept


Complete step-by-step solution:
In the problem the given equation is
$3x + 2y = 2$
We know the slope – intercept form.
The equation of a line in slope-intercept form is
$y = mx + b$
We have to rearrange the given equation in the slope intercept form so, subtract $3x$ from both sides
$3x + 2y - 3x = 2 - 3x$
Cancel the some values having the different signs, so we have,
$2y = 2 - 3x$
Arrange the equation like slope-intercept form,
$2y = - 3x + 2$
Divide the equation left hand side and right side by two
$\dfrac{{2y}}{2} = \dfrac{{ - 3x}}{2} + \dfrac{2}{2}$
Therefore we have a equation,
$y = \dfrac{{ - 3}}{2}x + 1$
This is the slope-intercept form of the given equation.

Note: The equation of a line can be written different ways; and each of these ways is valid. The slope intercept form of a line is a way of writing the equation of a line so that the slope of the line and the $y$-intercept are easily identifiable. The slope is the steepness of the line, and the $y$-intercept is the place the line crosses the $y$-axis. In mathematics the slope or gradient of a line is a number that describes both the direction and the steepness of the line slope is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points on a line.