Question

The equation of line p is y=(1)/(4)x-8. Line q, which is parallel to line p, includes the point (6,-3). What is the equation of line q ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

To find the equation of line q, which is parallel to line p, we use the point-slope form of a linear equation with the given point (6, -3) and the slope 1/4. Simplifying the equation gives us y = (1/4)x - 9/2 as the equation of line q in slope-intercept form.

Step-by-step explanation:

Given that line p has an equation of y = (1/4)x - 8, we know that its slope is 1/4. Since line q is parallel to line p, it will have the same slope.

Using the point-slope form of a linear equation, we can write the equation of line q using the point (6, -3) and the slope 1/4:

y - y1 = m(x - x1)

y - (-3) = (1/4)(x - 6)

Simplifying, we get:

y + 3 = (1/4)x - 3/2

y = (1/4)x - 9/2

Therefore, the equation of line q in slope-intercept form is y = (1/4)x - 9/2.

Answer 2

To find the equation of line q, which is parallel to line p, we can use the fact that parallel lines have the same slope. Line p has a slope of 1/4, so line q will also have a slope of 1/4. We are also given that line q includes the point (6, -3). T The equation of line q is y = 1/4x - 9/2.

Step-by-step explanation:

To find the equation of line q, which is parallel to line p, we can use the fact that parallel lines have the same slope. Line p has a slope of 1/4, so line q will also have a slope of 1/4. We are also given that line q includes the point (6, -3). Using the point-slope form of a linear equation, we can plug in the slope and the coordinates of the point to find the equation of line q:

y - y1 = m(x - x1)

y - (-3) = 1/4(x - 6)

y + 3 = 1/4x - 3/2

y = 1/4x - 3/2 - 3

y = 1/4x - 9/2

Therefore, the equation of line q is y = 1/4x - 9/2.