QQuestionMathematics
QuestionMathematics
Which equation matches the graph?
In the xy graph, the range of the x axis is minus eight to zero by increment of one. On both axes every alternate tick mark is labeled. On the graph there is a line passing through the points (- 6, 0) and (0, - 8).
A. 2x + 6y = –8
B. –2x + 6y = –8
C. 3x + 4y = –12
D. 4x + 3y = –24
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Answer
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Step 1:Find the slope using two points
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - 0}{0 - (-6)} = \frac{-8}{6} = -\frac{4}{3}
Calculate the slope of the line using the points (- 6, 0) and (0, - 8).
Step 2:Write the equation in point-slope form
y - y_1 = m(x - x_1) \Rightarrow y - 0 = -\frac{4}{3}(x + 6)
Use the slope and one point to write the equation.
Step 3:Convert to standard form
y = -\frac{4}{3}x - 8 \Rightarrow 3y = -4x - 24 \Rightarrow 4x + 3y = -24
Multiply both sides by 3 and rearrange to standard form.
Final Answer
\boxed{4x + 3y = -24}
The equation that matches the graph is option D.
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