Question
Write the equation of a line parallel to y = -
x + 3 and that goes through the point (4, -1)
- y + 1 =
(x - 4) - y - 1 = (x + 4)
- y + 1 = 2(x - 4)
- y - 1 = 2(x + 4)
(x - 4)(x + 4)
Hint:
We are given an equation of line. We have to find the equation of line that is parallel to the given line and passing through point (4,-1). We will use the properties of parallel lines to solve the question.
The correct answer is: y + 1 = (x - 4)
The given equation of line is y = 
x + 3
We have to find line parallel to this line.
Parallel lines have same slope.
To find the slope of the given line, we will compare the equation with slope-intercept form. The slope-intercept form of a line is y = mx + c. Here m is the slope of the line and c is the y-intercept.
Comparing the given equation of line with slope-intercept form we get,
m =
Now, we have a point through which line is passing and slope. We will use slope-point form to find the parallel line.
Slope-point form is (y – y1) = m(x – x1). Here y1 and x1 are the points through which line is passing. (x1 ,y1) ≡ (4,-1)
Substituting all the values
y + 1 = (x - 4)
This is the required equation.
For such questions, we should know different formulas required to find lines. We should also know the concept of slope of different lines.
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