QuestionQuestion
What is an equation of the line that passes through the point and is parallel to the line ?
Studdy Solution
STEP 1
1. We need to find the equation of a line.
2. The line must pass through the point .
3. The line must be parallel to the line given by the equation .
STEP 2
1. Determine the slope of the given line.
2. Use the point-slope form to write the equation of the new line.
3. Simplify the equation to the desired form.
STEP 3
Determine the slope of the given line.
The given line is . To find the slope, we need to rewrite this equation in slope-intercept form, , where is the slope.
Subtract from both sides:
The slope of the given line is .
STEP 4
Use the point-slope form to write the equation of the new line.
The point-slope form of a line is given by:
where is a point on the line, and is the slope. We know the line passes through and is parallel to the given line, so it has the same slope .
Substitute the point and slope into the point-slope form:
STEP 5
Simplify the equation to the desired form.
Distribute on the right side:
This is the equation of the line in slope-intercept form.
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