Questions: Find the intercepts, then graph the equation using two points. 5x + 2y = 30 a) Identify the x-intercept. Enter your answer as an ordered pair. If there is no x-intercept, enter None. x-intercept (6,0) b) Identify the y-intercept. Enter your answer as an ordered pair. If there is no y intercept, enter None. y-intercept (0,15) c) Graph the equation by entering the coordinates of two points below. Round to two decimal places if needed. Point 1: 0,0

Find the intercepts, then graph the equation using two points.
5x + 2y = 30
a) Identify the x-intercept. Enter your answer as an ordered pair. If there is no x-intercept, enter None.
x-intercept
(6,0)

b) Identify the y-intercept. Enter your answer as an ordered pair. If there is no y intercept, enter None.
y-intercept
(0,15)

c) Graph the equation by entering the coordinates of two points below. Round to two decimal places if needed.
Point 1: 0,0

Transcript text: Find the intercepts, then graph the equation using two points. \[ 5 x+2 y=30 \] a) Identify the $x$-intercept. Enter your answer as an ordered pair. If there is no $x$ intercept, enter None. x-intercept $(6,0)$ b) Identify the $y$-intercept. Enter your answer as an ordered pair. If there is no $y$ intercept, enter None. $y$-intercept $(0,15)$ c) Graph the equation by entering the coordinates of two points below. Round to two decimal places if needed. Point 1: 0,0

Solution

Solution Steps

Step 1: Find the $x$-intercept

To find the $x$-intercept, set $y = 0$ in the equation $5x + 2y = 30$.

\[ 5x + 2(0) = 30 \implies 5x = 30 \implies x = 6 \]

The $x$-intercept is $(6, 0)$.

Step 2: Find the $y$-intercept

To find the $y$-intercept, set $x = 0$ in the equation $5x + 2y = 30$.

\[ 5(0) + 2y = 30 \implies 2y = 30 \implies y = 15 \]

The $y$-intercept is $(0, 15)$.

Step 3: Choose two points to graph the equation

We already have two points from the intercepts: $(6, 0)$ and $(0, 15)$.

Final Answer

a) The $x$-intercept is $(6, 0)$.

b) The $y$-intercept is $(0, 15)$.

c) Two points to graph the equation are $(6, 0)$ and $(0, 15)$.

{"axisType": 3, "coordSystem": {"xmin": -1, "xmax": 7, "ymin": -1, "ymax": 16}, "commands": ["y = (-5/2)x + 15"], "latex_expressions": ["$5x + 2y = 30$"]}

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