Question

How do you find the slope and intercept of $ - 3x + 2y = 8$ ?

Answer 1

Hint: We will convert the given equation into standard form of an equation in slope-intercept form. The question deals with the slope and intercept of the lines. The given equation of line is in the form of the general equation of line. We will find the slope of the given equation of line by comparing it with the standard form of the equation of line.to find the intercept of the given line we need to compare the equation of the given line with the equation of the general form of line. The general equation of a line having slope of $m$ and intercepts on the coordinate axis $c$ is $y = mx + c$. $m$ is the slope of line and $c$ is the intercept made by the line on the $y - $axis. Slope is defined as the ratio of vertical change to the horizontal change. An intercept is defined as a point where the straight line or a curve intersects the axis in a plane. We can write the equation of a line perpendicular to a given line if we know a point on the line and the equation of the given line. The slopes of a parallel line are equal and if the two lines are parallel then the slope will be equal and they have different $y - $intercept. A vertical line will have no slope.

Complete step by step solution:
Step: 1 the given equation of line is $ - 3x + 2y = 8$ .
Convert the equation into standard form.
$ \Rightarrow y = \dfrac{3}{2}x + 4$
Compare the given equation of line with the general equation of line $y = mx + c$, where $m$ is slope of line and $c$ is the $y - $intercept of the line.
$
   \Rightarrow m = \dfrac{3}{2} \\
   \Rightarrow c = 4 \\
 $
Therefore, the slope of the line is 3 and $y - $intercept of the line is 10.
 Step: 2 to find the $x - $ intercept, substitute $y = 0$ in the equation.
$
   \Rightarrow y = \dfrac{3}{2}x + 4 \\
   \Rightarrow \dfrac{3}{2} \times x + 4 = 0 \\
   \Rightarrow x = - \dfrac{8}{3} \\
 $

Final Answer:
Therefore, the slope of the line is $\dfrac{3}{2}$ and $y - $intercept of the line is 4, $x - $ intercept is $ - \dfrac{8}{3}$.

Note:
Substitute the $x = 0$ in the equation of the given line to find the $y - $intercept of the line. We can also find the $y - $intercept of the line by comparing the equation with the standard form of equation of the line. Substitute $y = 0$ in the equation of line to find the $x - $intercept of the line.