Questions: Graph the equation -5x-2y=-11 by plotting points using the line tool.

Graph the equation -5x-2y=-11 by plotting points using the line tool.

Solution

Solution Steps

Step 1: Rewrite the Equation in Slope-Intercept Form

To graph the equation, we first need to rewrite it in the slope-intercept form, $ y = mx + b $.

Starting with the given equation: \[ -5x - 2y = -11 \]

Solve for $ y $: \[ -2y = 5x - 11 \]

Divide every term by $-2$: \[ y = -\frac{5}{2}x + \frac{11}{2} \]

Step 2: Identify the Slope and Y-Intercept

From the equation $ y = -\frac{5}{2}x + \frac{11}{2} $, we can identify:

The slope $ m = -\frac{5}{2} $
The y-intercept $ b = \frac{11}{2} $

Step 3: Plot Points and Draw the Line

To graph the line, we can use the y-intercept and the slope:

Start at the y-intercept $(0, \frac{11}{2})$.
Use the slope to find another point. From $(0, \frac{11}{2})$, move down 5 units and right 2 units to reach the point $(2, \frac{1}{2})$.

Final Answer

The equation in slope-intercept form is $ y = -\frac{5}{2}x + \frac{11}{2} $.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (-5/2)x + (11/2)"], "latex_expressions": ["$y = -\\frac{5}{2}x + \\frac{11}{2}$"]}

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