Question

Which equation represents a line that passes through the points (7, 5) and (6, 1)?

Multiple choice question.
cross out
A) y – 1= –4(x – 6)
cross out
B) y – 5=4(x – 7)
cross out
C) y – 6= –4(x – 1)
cross out
D) y – 7=4(x – 5)

Answer 1

To find the equation of a line that passes through two given points, use the point-slope form and the slope formula. By applying these to the points (7, 5) and (6, 1), the correct equation of the line is y - 5 = 4(x - 7), hence the answer is option B.

Step-by-step explanation:

The question is asking for the equation of a line that passes through two given points. To find the equation of a line, one can use the point-slope form which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).

To find the slope of the line that passes through the points (7, 5) and (6, 1), we use the formula and get m = (1 - 5)/(6 - 7) = -4/(-1) = 4. Thus, the slope m is 4, and one of the given points, say (7, 5), can be used in the point-slope form to write the equation.

Using the point-slope form:

1. Solving for y using y - 5 = 4(x - 7) by distributing 4 into (x - 7) we get y - 5 = 4x - 28,
2. Adding 5 to both sides gives us y = 4x - 23 which is the standard form of a linear equation.

This correctly represents the line that passes through the points (7, 5) and (6, 1). Therefore, the correct answer is B) y - 5 = 4(x - 7).