Questions: Sketch the graph of the equation and label its intercepts. 5 x+3 y=10 Identify the intercepts of the graph. The x-intercept is The y-intercept is (Type integers or simplified fractions.)

$Sketch the graph of the equation and label its intercepts. 5 x+3 y=10 Identify the intercepts of the graph. The x-intercept is The y-intercept is (Type integers or simplified fractions.)$

Transcript text: Sketch the graph of the equation and label its intercepts. \[ 5 x+3 y=10 \] Identify the intercepts of the graph. The $x$-intercept is $\square$ The $y$-intercept is $\square$ (Type integers or simplified fractions.)

Solution

Solution Steps

Step 1: Find the x-intercept

To find the x-intercept, set $ y = 0 $ in the equation $ 5x + 3y = 10 $.

\[ 5x + 3(0) = 10 \implies 5x = 10 \implies x = \frac{10}{5} = 2 \]

The x-intercept is $ 2 $.

Step 2: Find the y-intercept

To find the y-intercept, set $ x = 0 $ in the equation $ 5x + 3y = 10 $.

\[ 5(0) + 3y = 10 \implies 3y = 10 \implies y = \frac{10}{3} \]

The y-intercept is $ \frac{10}{3} $.

Final Answer

The x-intercept is $ 2 $.
The y-intercept is $ \frac{10}{3} $.

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = (-5/3)x + 10/3"], "latex_expressions": ["$5x + 3y = 10$"]}

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