Answer:
B. y = 2x - 2
E. [tex] y + 4 = 2(x + 1) [/tex]
F. [tex] y - 6 = 2(x - 4) [/tex]
Step-by-step explanation:
The equation of the line can be found using either the point-slope equation or the slope-intercept equation.
✔️Equation of the line in point-slope using the slope and the coordinates of the point (4, 6):
Slope = m = change in y/change in x
Using (4, 6) and (-1, -4),
m = (-4 - 6)/(-1 - 4)
m = -10/-5
m = 2
Substitute m = 2, and (a, b) = (4, 6) into the point-slope equation form [tex] y - b = m(x - a) [/tex]
Thus:
[tex] y - 6 = 2(x - 4) [/tex]
✔️Equation of the line in point-slope using the slope and the coordinates of the point (-1, -4):
Slope = m = 2
Substitute m = 2, and (a, b) = (-1, -4) into the point-slope equation form [tex] y - b = m(x - a) [/tex]
Thus:
[tex] y - (-4) = 2(x - (-1)) [/tex]
[tex] y + 4 = 2(x + 1) [/tex]
✔️Equation of the line in slope-intercept form, y = mx + b
Where,
m = slope = 2
b = y-intercept = -2 (the point where the line intercepts the y-axis)
Thus, substitute m = 2 and b = -2 into y = mx + b
y = 2x + (-2)
y = 2x - 2
