Question

The equation of line u is y-4=- 4/5 (x+3). Line v includes the point (7,-6) and is parallel to line u. What is the equation of line v? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

Line v is parallel to line u and thus has the same slope of -4/5. By substituting point (7, -6) into the slope-intercept form with the slope, the y-intercept (b) for line v is calculated to be -2/5. The equation for line v is y = -4/5x - 2/5.

Step-by-step explanation:

The subject of this question is to find the equation of line v, which is parallel to line u.

The given equation of line u is y - 4 = -4/5(x + 3). Since line v is parallel to line u, it will have the same slope, which is -4/5. We use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Because line v passes through the point (7, -6), we can substitute (7, -6) into the slope-intercept form along with the slope -4/5 to find b, the y-intercept, for line v.

Begin by substituting into the slope-intercept form:

• -6 = (-4/5)(7) + b

Solve the equation for b by multiplying -4/5 by 7 and adding the result to -6:

• -6 = (-4/5)(7) + b
• -6 = -28/5 + b
• b = -6 + 28/5
• b = -30/5 + 28/5
• b = -2/5

Now that we have the y-intercept, we can write the equation for line v as:

• y = -4/5x - 2/5