Given:
3x - 5y = 18
To graph this line, rewrite the equation in slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Subtract 3x from both sides:
3x - 3x - 5y = -3x + 18
-5y = -3x + 18
Divide all terms by -5:
[tex]\begin{gathered} \frac{-5y}{-5}=\frac{-3x}{-5}+\frac{18}{-5} \\ \\ y=\frac{3}{5}x-\frac{18}{5} \end{gathered}[/tex]Thus, the slope intercept form of the equation is:
[tex]y=\frac{3}{5}x-\frac{18}{5}[/tex]Any line can be graphed using two or more points.
Let's determine two points on the line.
Input 6 for x and solve for y:
[tex]\begin{gathered} y=\frac{3}{5}\ast6-\frac{18}{5} \\ \\ y=\frac{18}{5}-\frac{18}{5} \\ \\ y=0 \end{gathered}[/tex]Also, the y-intercept is:
[tex](0,-\frac{18}{5})[/tex]convert the fraction to decimal:
[tex]-\frac{18}{5}=-3.6[/tex]Thus, we have the points:
[tex]\begin{gathered} (0,-3.6) \\ (6,\text{ 0)} \end{gathered}[/tex]x y
0 -3.6
6 0
Mark the points on a graph and make a straight line that passes through the points.
The graph is attached below:
