find the equation of a line whose slope is 8 and pass through the point (-2,1)
a). y=8x-2
b). y=8x 17
c). y=9-2x
d). y=x 6?
(-2, 1), m = 8.
Y = mx + b.
1 = 8*(-2) + b,
b = 17.
Y = 8x + 17.
To find the equation of a line with a given slope passing through a specific point, we can use the point-slope form of a linear equation.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m represents the slope.
In this case, the slope is 8 and the point is (-2,1).
Substituting these values into the point-slope form, we have:
y - 1 = 8(x - (-2))
Simplifying further:
y - 1 = 8(x + 2)
Expanding the brackets:
y - 1 = 8x + 16
To isolate y, we add 1 to both sides of the equation:
y = 8x + 17
Thus, the equation of the line with a slope of 8 passing through the point (-2,1) is given by option b): y = 8x + 17.
To find the equation of a line given its slope and a point it passes through, we can use the point-slope form of a linear equation. The point-slope form is written as:
y - y1 = m(x - x1)
Where:
- y1 and x1 are the coordinates of the given point through which the line passes.
- m is the slope of the line.
In this case, the slope (m) is 8, and the point (-2, 1) lies on the line. Substituting these values into the point-slope form, we get:
y - 1 = 8(x - (-2))
Simplifying the equation:
y - 1 = 8(x + 2)
Expanding the expression inside the parentheses:
y - 1 = 8x + 16
Finally, adding 1 to both sides of the equation, we obtain:
y = 8x + 17
Therefore, the correct answer is:
b). y = 8x + 17