Write an equation in slope-intercept form of the line through point P(6, –1) with slope 4.
A. y = 4x – 25
B. y + 6 = 4(x – 1)
C. y + 1 = 4(x – 6)
D. y = 4x – 1
How would I do this?
It's A. y = 4x – 25
I go that, but it was graded as wrong! :( which is why I'm confused
maybe it is B?
To find an equation in slope-intercept form (y = mx + b) of a line passing through a given point and with a given slope, you can use the point-slope form of a line.
The point-slope form of a line is given by: y - y₁ = m(x - x₁)
To use this formula, substitute the slope (m) and the coordinates of the given point (x₁, y₁) into the equation.
In this case, the given point is P(6, -1) and the given slope is 4.
Substituting the values into the point-slope form equation, we get:
y - (-1) = 4(x - 6)
Simplifying the equation:
y + 1 = 4(x - 6)
Re-arranging the equation to the slope-intercept form, we isolate y:
y = 4(x - 6) - 1
Expanding the right side of the equation:
y = 4x - 24 - 1
Simplifying further:
y = 4x - 25
Therefore, the correct equation in slope-intercept form for the line passing through point P(6, –1) with a slope of 4 is:
A. y = 4x - 25
first, review the point-slope form. It relies on the fact that the slope of a line is constant. So, the slope between any two points is always the same. So, pick any point (x,y) on the line and use the definition of the slope to see that
(y-(-1))/(x-6) = 4
Or, more usually it is written
y+1 = 4(x-6)