2.8k views
2 votes
What is the equation of the line in slope-intercept form that passes through the point (-3, 0) and is parallel to the line represented by y + 4 = 7(x - 12)?

a. y = -1/7x - 3
b. y = 7x + 21
c. y = 7x - 3
d. y = -1/7x - 3/7

1 Answer

5 votes

Final answer:

To find the equation of a line in slope-intercept form that is parallel to a given line and passes through a given point, we use the point-slope form. First, we rearrange the given equation into slope-intercept form to find the slope and y-intercept. Then, we use the point-slope form with the slope and the given point to find the equation of the line. The equation of the line parallel to y + 4 = 7(x - 12) that passes through (-3, 0) is y = 7x + 21, which is option b.

Step-by-step explanation:

The equation of the line parallel to y + 4 = 7(x - 12) and passing through the point (-3, 0) can be found by first writing the given equation in slope-intercept form to find the slope. The original equation simplifies to y = 7x - 88, so the slope is 7. Since parallel lines have the same slope, the parallel line will also have a slope of 7. To find the y-intercept of the new line, we can use the point (-3, 0) and the slope (7) in the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point (-3, 0) and m is the slope 7. Plugging in these values, we get y - 0 = 7(x - (-3)), y = 7x + 21. Therefore, the equation in slope-intercept form is y = 7x + 21, which corresponds to option b.

User Lyubomyr Dutko
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories