Math Problem Statement
Which equation in standard form has a graph that passes through the point (−4, 2)(−4, 2) and has a slope of 9292 ?
A.9x−2y=369x−2y=36
B.9x−2y=269x−2y=26
C.9x−2y=−409x−2y=−40
D.9x−2y=−109x−2y=−10
Solution
To determine which equation in standard form represents the line that passes through the point and has a slope of , we need to use the point-slope form of the equation of a line and convert it to standard form.
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Point-slope form of the equation: where is a point on the line and is the slope.
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Substituting and into the point-slope form:
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Simplify and convert to slope-intercept form:
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Convert to standard form : Multiply every term by 2 to eliminate the fraction: Rearrange to standard form:
Thus, the correct equation in standard form is:
So, the correct answer is: C. 9x - 2y = -40
Would you like details or have any questions?
Here are 5 related questions to expand your understanding:
- How do you convert an equation from slope-intercept form to standard form?
- What is the point-slope form of a line, and when is it useful?
- Can you explain the process of finding the slope of a line given two points?
- How do you determine if a point lies on a given line?
- What are the differences between different forms of linear equations (slope-intercept, point-slope, standard)?
Tip: Always check your work by substituting the given point into your final equation to ensure it satisfies the equation.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Point-Slope Form
Standard Form of a Line
Formulas
Point-Slope form: y - y1 = m(x - x1)
Slope-Intercept form: y = mx + b
Standard form: Ax + By = C
Theorems
Linear Equation Conversion
Suitable Grade Level
Grades 9-11
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