Question

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line y = −3x + 6, point (1, −5)

Short answer

Equation of the parallel line to the line $y=-3x+6$passing through the point (1, -5) is$y=-3x-2$.

Step-by-step solution

Step 1. Given information

We have given equation of the line is,

$y=-3x+6$and point is (1, -5).

Step 2. Concept

Here we can use the slope - point formula and slope intercept formula.

Slope - point formula: $y-y_1=m(x-x_1)$

Slope - intercept formula: $y=mx+b$

Where, m is the slope, b is the y - intercept.

$(x_1,y_1)$is the one of the given point.

Step 3. Explanation

We have given equation of the line is,

$y=-3x+6$comparing it with slope - intercept form $y=mx+b$we get slope of the line is m = -3.

We know that two lines are parallel if their slopes are equal and they have different y-intercepts.

Hence, slope of the parallel line is same as the slope of the given line.

Using slope - intercept formula,

$y-y_1=m(x-x_1)$

Substituting given point and slope,

$y-(-5)=-3(x-1)$

role="math" localid="1644309581491" $\Rightarrow y=-3x-2$

Step 4. Conclusion

Hence, equation of the parallel line to the line $y=-3x+6$passing through the point (1, -5) is$y=-3x-2$.