Question

consider the following equation.
\\(3y - 5x = \frac{-15}{2}\\)
step 2 of 2 : graph the equation by plotting the \\(x\\)- and \\(y\\)-intercepts. if an intercept does not exist, or is duplicated, use another point on the line to plot the graph.
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Explanation:

Step1: Find x-intercept (set y=0)

Set $y=0$, solve for $x$:
$$3(0) - 5x = \frac{-15}{2}$$
$$-5x = \frac{-15}{2}$$
$$x = \frac{-15/2}{-5} = \frac{3}{2} = 1.5$$
x-intercept: $(1.5, 0)$

Step2: Find y-intercept (set x=0)

Set $x=0$, solve for $y$:
$$3y - 5(0) = \frac{-15}{2}$$
$$3y = \frac{-15}{2}$$
$$y = \frac{-15/2}{3} = \frac{-5}{2} = -2.5$$
y-intercept: $(0, -2.5)$

Step3: Verify with a third point

Choose $x=3$, solve for $y$:
$$3y - 5(3) = \frac{-15}{2}$$
$$3y - 15 = \frac{-15}{2}$$
$$3y = 15 - \frac{15}{2} = \frac{15}{2}$$
$$y = \frac{15/2}{3} = \frac{5}{2} = 2.5$$
Third point: $(3, 2.5)$

Answer:

Plot the points $(1.5, 0)$, $(0, -2.5)$, and $(3, 2.5)$ on the coordinate plane, then draw a straight line through them to graph the equation.