Grant wrote an equation of a line through the point (4,1) that is perpendicular to the one shown. What other point lies on his line?
I have to see the line shown. We need the slope of the line shown.
Grant's line will have a slope that is a negative reciprocal of the line shown.
for example if the line has a slope of -3, Grant's perpendicular line will be 1/3.
To find the other point, use the slope formula: m = (y2-y1)/(x2-x1)
Another approach is to use:
y = mx + b
You will have m, x and y.
solve for b.
Write an equation where you have a value for m and b.
You can then figure out another x and y that will work in that equation.
To find the other point that lies on the line through (4,1) perpendicular to the given line, we first need to determine the equation of the given line.
If we know the equation of a line, we can easily find its slope. The given line is not provided, so without further information, it is not possible to determine the slope of the given line directly.
However, we are given that the line we are looking for is perpendicular to the given line. In geometry, perpendicular lines have slopes that are negative reciprocals of each other. Thus, if the slope of the given line is m, the slope of the perpendicular line will be -1/m.
Now, let's assume that the equation of the given line is of the form y = mx + b, where m is the slope. We know that the line we are looking for is perpendicular, so its equation will be in the form y = (-1/m)x + b, with the same y-intercept b.
Since the line we are looking for passes through the point (4,1), we can substitute these coordinates into the equation. This will allow us to solve for b.
Using the point (4,1), we have:
1 = (-1/m)(4) + b
Now, we have an equation with one unknown (b), and we can solve for it by rearranging the equation:
1 = -4/m + b
1 + 4/m = b
Now that we know the y-intercept (b), we can write the equation of the line as:
y = (-1/m)x + (1 + 4/m)
With this equation, we have the line perpendicular to the given line that passes through the point (4,1). To find another point on this line, we can choose any value for x and substitute it into the equation to solve for y. For example, if we choose x = 0, we can calculate y:
y = (-1/m)(0) + (1 + 4/m)
y = 1 + 4/m
So, another point on the line is (0, 1 + 4/m).