Question

question 4 of 10, step 2 of 2
consider the following equation.
7y - 6x = -21
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.
answer
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Explanation:

Step1: Find x-intercept (y=0)

Substitute $y=0$ into $7y - 6x = -21$:
$$7(0) - 6x = -21$$
$$-6x = -21$$
$$x = \frac{-21}{-6} = \frac{7}{2} = 3.5$$
x-intercept: $(3.5, 0)$

Step2: Find y-intercept (x=0)

Substitute $x=0$ into $7y - 6x = -21$:
$$7y - 6(0) = -21$$
$$7y = -21$$
$$y = \frac{-21}{7} = -3$$
y-intercept: $(0, -3)$

Step3: Verify with a third point

Choose $x=7$, substitute into the equation:
$$7y - 6(7) = -21$$
$$7y - 42 = -21$$
$$7y = 21$$
$$y = 3$$
Third point: $(7, 3)$

Answer:

Plot the points $(3.5, 0)$, $(0, -3)$, and $(7, 3)$, then draw a straight line through them to graph the equation.