Which equation is the equation of a line that passes through (–10, 3) and is perpendicular to y = 5x – 7?
y = 5x + 53
y = –x – 7
y = –x + 1
y = x + 5
Help - I don't understand...being told it is C but why?
you should be able to see that the slope of y = 5x-7 is 5, right?
so, the perpendicular line has slope -1/5.
None of the choices has slope -1/5.
ok....thank you
The answer is y=-1/5x+1
To determine which equation represents a line that passes through the point (-10, 3) and is perpendicular to y = 5x – 7, we need to understand the concept of perpendicular lines.
Perpendicular lines have slopes that are negative reciprocals of each other. The given equation, y = 5x – 7, is in slope-intercept form (y = mx + b), where the slope (m) is 5. Therefore, to find the perpendicular line, we need to determine its slope.
The negative reciprocal of 5 is -1/5. Thus, the perpendicular line will have a slope of -1/5.
Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) represents the given point and m represents the slope. Plugging in the values (-10, 3) and -1/5 for (x1, y1) and m respectively, we get:
y - 3 = -1/5(x - (-10))
Simplifying,
y - 3 = -1/5(x + 10)
Expanding the equation and converting it to slope-intercept form, we get:
y = -1/5x - 2 + 3
y = -1/5x + 1
Now, comparing this equation with the given options, we can see that the equation y = -x + 1 (option C) matches our result. Therefore, the equation of the line that passes through (-10, 3) and is perpendicular to y = 5x – 7 is y = -x + 1.