Question

Write an equation for the line parallel to the given line that contains point C(1,4) where the original line is y = 7x + 4.

a) y = 7x - 3
b) y = 7x + 4
c) y = 4x + 7
d) y = -7x + 11

Answer 1

(a)

Step-by-step explanation:

given the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the original line with equation

y = 7x + 4 ← in slope- intercept form

with slope m = 7

• Parallel lines have equal slopes , then

y = 7x + c ← is the partial equation

to find c , substitute C (1, 4 ) for x and y into the partial equation

4 = 7(1) + c = 7 + c ( subtract 7 from both sides )

- 3 = c

y = 7x - 3 ← equation of parallel line

Answer 2

To find the equation for a line parallel to y = 7x + 4 passing through point C(1,4), use point-slope form and plug in the slope and the coordinates of point C. The correct equation is y = 7x - 3.

Step-by-step explanation:

To find an equation for the line parallel to y = 7x + 4 that contains point C(1,4), we need to keep the same slope as the original line, which is 7, and plug in the coordinates of point C into the equation y = mx + b, where m is the slope and b is the y-intercept.

Using point-slope form, we have y - y1 = m(x - x1), where (x1, y1) are the coordinates of point C. Substituting the values, we get y - 4 = 7(x - 1). Simplifying, we have y - 4 = 7x - 7. Adding 4 to both sides, we obtain y = 7x - 3.

Therefore, the equation for the line parallel to y = 7x + 4 that contains point C(1,4) is y = 7x - 3, so the correct answer is a) y = 7x - 3.