Answer:
The equation of the line that has a slope of -2 and y-intercept of 1 will be:
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given
The slope m = -2
y-intercept b = 1
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
It is already stated that the y-intercept = -1
It means at y = 1, x = 0
Thus, we have the point (0, 1)
Now using the slope-intercept form
y = mx+b
substituting m = -2 and b = 1
y = -2x + (1)
y = -2x+1
Therefore, the equation of the line that has a slope of -2 and y-intercept of 1 will be:
has gradient
which at the point (-1, 4, 3) has a value of
I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say , in which case we have
Then the derivative of at (-1, 4, 3) in the direction of
is