Math Problem Statement
5y−8=−2(4−x)5𝑦−8=−2(4−𝑥)
Step 2 of 2 :
Find the equation of the line which passes through the point (11,13)(11,13) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer.
Solution
Step 1: Solve the given equation for
You are given the equation:
Distribute the on the right-hand side:
Next, add to both sides to isolate the term with :
Now, divide both sides by 5 to solve for :
This is the equation of the given line in slope-intercept form, , where the slope .
Step 2: Find the equation of the line parallel to the given line
Since the new line is parallel to the given line, it will have the same slope, . Now, use the point to find the equation of the line that passes through this point.
We will use the point-slope form of a line:
where , , and . Substituting these values into the equation:
Distribute on the right-hand side:
Next, add to both sides to solve for . First, express 13 as a fraction with the denominator 5:
Simplifying:
Final Answer
The equation of the line that passes through the point and is parallel to the given line is:
Would you like more details or have any questions? Here are 5 related problems you can try:
- Find the equation of a line that passes through and is parallel to .
- Find the equation of a line passing through and perpendicular to .
- What is the slope of a line parallel to the line ?
- Find the slope of a line perpendicular to the line with equation .
- Determine the point where the line intersects the y-axis.
Tip: When two lines are parallel, they always share the same slope.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Point-Slope Form
Parallel Lines
Formulas
Slope-intercept form: y = mx + b
Point-slope form: y - y1 = m(x - x1)
Theorems
Parallel lines have equal slopes
Suitable Grade Level
Grades 9-10
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