Question

Write the equation of a line that is parallel to y = -0.75x and that passes through the point (8,0)

A) y = -0.75x + 6
B) y = -0.75x - 6
C) y = 0.75x + 6
D) y = 0.75x - 6

Answer 1

The equation of the line parallel to y = -0.75x that passes through (8,0) is y = -0.75x + 6, which is option A.

Step-by-step explanation:

The student is asking for the equation of a line that is parallel to y = -0.75x and passes through the point (8,0). Lines that are parallel to each other have the same slope. The slope of the given line is -0.75. Therefore, the slope of our new line must also be -0.75. To find the y-intercept, we use the point given through which the line passes. Plugging in the values into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we get 0 = (-0.75)(8) + b. Solving for b gives us b = 6. Therefore, the equation of the line parallel to y = -0.75x passing through (8,0) is y = -0.75x + 6, which corresponds to option A).

Answer 2

The correct equation of a line that is parallel to y = -0.75x and passes through the point (8,0) is A) y = -0.75x + 6, determined by maintaining the same slope as the original line and solving for the y-intercept using the given point.

Step-by-step explanation:

To find the equation of a line that is parallel to y = -0.75x and passes through the point (8,0), we should use the same slope as the given line, because parallel lines have equal slopes. The slope of the given line is -0.75. Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we plug in our slope and the point to solve for b.

Using the point (8,0): y = -0.75x + b becomes 0 = -0.75(8) + b. Solving for b gives b = 6, so the equation of our line is y = -0.75x + 6. Therefore, the correct answer is A) y = -0.75x + 6.