The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y plus 7 equals negative StartFraction 2 over 5 EndFraction left-parenthesis x minus 10 right-parenthesis.. What is the standard form of the equation for this line?
2x – 5y = –15
2x – 5y = –17
2x + 5y = –15
2x + 5y = –17
(-5, -1), (10, -7).
Y = mx + b.
m = (-7+1)/(10+5) = -6/15 = -2/5.
b = y-mx = -1-(-2/5(-5) = -1 - 2 = -3.
Y = -2x/5 - 3.
2x/5 + y = -3,
2x + 5y = -15.
The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?
To find the standard form of the equation for the line, we need to convert the given point-slope form into standard form (Ax + By = C) by rearranging the equation.
The point-slope form of the equation is given as:
y + 7 = (-2/5)(x - 10)
To convert this into standard form, we need to eliminate the fraction and simplify the equation further.
Multiply both sides of the equation by 5 to eliminate the fraction:
5(y + 7) = -2(x - 10)
Distribute on both sides:
5y + 35 = -2x + 20
Rearrange the equation to put it in the standard form:
2x + 5y = -15
So, the standard form of the equation for the line is 2x + 5y = -15. Therefore, the correct answer is:
2x + 5y = -15.
Why not just say:
y+7 = (-2/5)(x-10) , instead of that gibberish ??
steps:
multiply each side by 5
further expand the right side
make sure all terms x and y are on the left side, and the constant is on the right side.
Pick the matching answer, all done