I need to write an equation of the line containing the given point and parallel to the given line in y=mx+b form (7,9);x+4y=7......can you please help me find the solution

easiest way:

since the two lines are parallel, they will differ only in the constant.
so let the new line by x + 4y = k
but (7,9) lies on it
so 7 + 4(9) = k
k = 43 for an equation of x + 4y = 43

change to y = mx + b form
4y = -x + 43
y = (1/4)x + 43/4

On three consecutives passes, a football team gains 7 yards, loses 19 yards, and gains 38 yards. What number represents the total net yardage?

To write an equation in the form y = mx + b, where m is the slope and b is the y-intercept, we need to find the slope of the given line and the y-intercept of the new line.

Given: point (7,9) and the line x + 4y = 7.

Step 1: Convert the given equation into slope-intercept form (y = mx + b).
x + 4y = 7

Subtract x from both sides:
4y = -x + 7

Divide both sides by 4:
y = (-1/4)x + 7/4

Now, we have the equation in slope-intercept form, y = mx + b, with m = -1/4 and b = 7/4.

Step 2: Since the new line is parallel to the given line, it will have the same slope (-1/4).

Step 3: Now we have the point (7,9) and the slope (-1/4). Using the point-slope form, we can find the equation of the parallel line.
y - y1 = m(x - x1)

Substituting the values:
y - 9 = (-1/4)(x - 7)

Distributing -1/4 to (x - 7):
y - 9 = (-1/4)x + 7/4

Rearranging the equation to match y = mx + b form:
y = (-1/4)x + 7/4 + 9

Combining like terms:
y = (-1/4)x + 28/4 + 36/4

y = (-1/4)x + 64/4

Simplifying the fraction, we get:
y = (-1/4)x + 16

Therefore, the equation of the line containing the point (7,9) and parallel to the line x + 4y = 7 is y = (-1/4)x + 16.