Write en rquation for the line passing through point (3,3) and parallel to the line whose equation is y=-(1)/(6)x+7

Answer:

y = - x +

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the line with equation

y = - x + 7 ← in slope- intercept form

with slope m = -

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c, substitute the point (3, 3 )  for x/ y into the partial equation

3 = - (3) + c = - + c ( add to both sides )

+ = c , that is

c =

y = - x + ← equation of parallel line

Final answer:

The equation of the line passing through point (3,3) and parallel to y = -(1/6)x + 7 is y = -(1/6)x + 3.5, which is achieved by knowing that parallel lines have the same slope and substituting the coordinates of the given point into the y = mx + b (slope-intercept form) and solving for the y-intercept 'b'.

Explanation:

The question asks for an equation of a line that is parallel to the equation y = -(1/6)x + 7 and also passes through the point (3,3). First, it's significant to understand that parallel lines share the same slope. Looking at the equation y = -(1/6)x + 7, we can see that the slope, or 'm' value, is -1/6. Therefore, the slope of our new line will also be -1/6. The conventional form of the equation for a line is y = mx + b where m is the slope and b is the y-intercept. Since we know the slope and have a point that lies on the line, we can substitute these values into this formula to solve for 'b'.

Here's how we do it:

First, substitute the point's coordinates into the equation for the line: 3 = (-1/6)*3 + b

This simplifies to: 3 = -1/2 + b

Then solving for 'b', we get: b = 3 + 1/2 = 3.5

Therefore, the equation of our new line that is parallel to the original line and passes through the point (3,3) is y = -(1/6)x + 3.5.

Learn more about Equation of a parallel line here:

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