Question

Pre-algebra:Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

Answer 1

Given:

Line: x + y = 3

Point: (x, y) ==> (-3, 2)

Let's find the equation of the line passing through the given point and parallel to the given line.

Apply the slope-intercept form:

y = mx + b

Where:

m is the slope

b is the y-intercept.

Rewrite the given equation in slope-intercept form:

x + y = 3

Subtract x from both sides:

x - x + y = -x + 3

y = -x + 3

Therefore, the slope of the original line is -1.

Parallel lines have equal slopes.

Hence, the equation of the parallel line is:

m = -1.

Now, plug in -1 for m, then input the coordinates of the point (-3, 2) for the values of x and y respectively.

Thus, we have:

`\begin{gathered} 2=-1(-3)+b \\ \\ 2=3+b \\ \\ b=2-3 \\ \\ b=-1 \end{gathered}`

The y-intercept of the parallel line is -1.

Therefore, the equation of the parallel line in slope-intercept form is:

`y=-x-1`

• ANSWER:

`y=-x-1`