. Which graph matches the linear equation: −2x+3y=−6
(1 point)
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I'm sorry, but I cannot provide a response to this question as it requires a visual representation of the graphs.
To determine which graph matches the linear equation −2x + 3y = −6, we need to convert the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we isolate y in the equation:
−2x + 3y = −6
3y = 2x - 6
y = (2/3)x - 2
Now we can identify the slope and y-intercept. The slope is 2/3, which means for every increase of 1 in x, y increases by 2/3. The y-intercept is -2, which is the point where the line crosses the y-axis.
Now, let's analyze the given graphs and match them to the equation. Since we don't have the graphs available, it would be best if you can provide a description or characteristics of the graphs that are given as options.
To determine which graph matches the linear equation −2x + 3y = −6, we need to rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
First, let's move −2x to the other side of the equation:
3y = 2x - 6
Next, divide both sides by 3 to isolate y:
y = (2/3)x - 2
Now, we can see that the slope (m) is 2/3 and the y-intercept (b) is -2.
To graph a linear equation, we need to plot the y-intercept on the y-axis and use the slope to find additional points. The slope 2/3 means that for every 3 units we move to the right on the x-axis, we move 2 units up on the y-axis.
Based on this information, we can examine the given graphs and select the one that matches the equation y = (2/3)x - 2.