Question

The equation for line k can be written as y - 8 = -8/3(x + 6). Line includes the point (-8,-5) and is perpendicular to line k. What is the equation of line ?

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

Answer:y - 8 = -8/3(x + 6)

To find the equation of a line perpendicular to line k that passes through the point (-8, -5), we can first determine the slope of line k, and then find the negative reciprocal of that slope to get the slope of the perpendicular line.

The slope of line k is the coefficient of x in its equation, which is -8/3.

The negative reciprocal of -8/3 is 3/8. So, the slope of the perpendicular line is 3/8.

Now that we have the slope (m = 3/8) and a point (-8, -5) that the line passes through, we can use the point-slope form of a line to find its equation:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point (-8, -5) and m is the slope (3/8).

Plugging in the values:

y - (-5) = (3/8)(x - (-8))

Simplify the equation:

y + 5 = (3/8)(x + 8)

Now, let's write this equation in slope-intercept form (y = mx + b) by isolating y:

y + 5 = (3/8)(x + 8)

y + 5 = (3/8)x + (3/8)(8)

y + 5 = (3/8)x + 3

Subtract 5 from both sides to isolate y:

y = (3/8)x + 3 - 5

y = (3/8)x - 2

So, the equation of the line perpendicular to line k that passes through the point (-8, -5) is:

y = (3/8)x - 2

Step-by-step explanation: Start with the equation of line k, given as:

y - 8 = -8/3(x + 6)

Determine the slope of line k, which is the coefficient of x in its equation. In this case, it's -8/3.

Find the negative reciprocal of the slope of line k to get the slope of the perpendicular line. The negative reciprocal of -8/3 is 3/8.

Now that you have the slope (m = 3/8) and a point (-8, -5) that the line passes through, use the point-slope form of a line:

y - y₁ = m(x - x₁)

Plug in the values:

y - (-5) = (3/8)(x - (-8))

Simplify the equation:

y + 5 = (3/8)(x + 8)

To write the equation in slope-intercept form (y = mx + b), isolate y:

y + 5 = (3/8)x + (3/8)(8)

Further simplify:

y + 5 = (3/8)x + 3

Subtract 5 from both sides to isolate y:

y = (3/8)x + 3 - 5

Finally, simplify the equation:

y = (3/8)x - 2

Answer 2

`\sf y =(3)/(8)x -2`

Explanation:

The slope of line k is -8/3.

Since line is perpendicular to line k, its slope is the negative reciprocal of -8/3, which is 3/8.

We can use the point-slope form of linear equations to find the equation of line l:

`\sf y - y_1 = m(x - x1)`

where (x1, y1) is the point (-8, -5) and m is the slope 3/8. Substituting, we get:

`\sf y - (-5) =(3)/(8)(x - (-8))`

Distribute 3/8, we get

`\sf y +5 =(3)/(8)x +3`

Subtract 5 on both sides,

`\sf y +5-5 =(3)/(8)x +3-5`

`\sf y =(3)/(8)x -2`

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

`\sf y =(3)/(8)x -2`