This question concerns the straight line that passes through the points (−1, 3) and (2, −6). Choose the three true statements from the following.
Options
A)
The gradient of the line is 3.
B)
The gradient of the line is −3.
C)
The gradient of the line is
1/3.
D)
The equation of the line is y = −3x.
E)
The equation of the line is y =2x − 6.
F)
The line cuts the y-axis at y =3.
G)
The line passes through the origin.
H)
The line passes through the point (1, −1).
(−1, 3) and (2, −6)
(-6 -3)/(2+1) = slope(or gradient) = -9/3 = -3
therefore
y = -3 x + b
3 = -3(-1) + b
b = 0
so
y = -3x
this goes through (0,0)
i need help
To find the gradient (slope) of the line passing through two points, we use the formula:
gradient = (change in y) / (change in x)
Let's calculate the gradient using the given points (-1, 3) and (2, -6):
change in y = -6 - 3 = -9
change in x = 2 - (-1) = 3
gradient = (-9) / 3 = -3
Now, we can examine each statement individually:
A) The gradient of the line is 3.
False. The gradient we calculated is -3, not 3.
B) The gradient of the line is -3.
True. The calculated gradient is -3.
C) The gradient of the line is 1/3.
False. The calculated gradient is -3, not 1/3.
D) The equation of the line is y = -3x.
False. The slope-intercept form of the equation is y = mx + c, where m is the gradient and c is the y-intercept. The gradient we calculated is -3, but we do not have the value of the y-intercept.
E) The equation of the line is y = 2x - 6.
True. To check this, we can substitute one of the given points into the equation. Let's use (-1, 3):
3 = 2(-1) - 6
3 = -2 - 6
3 = -8 (False)
Since the equation does not hold for one of the given points, this statement is false.
F) The line cuts the y-axis at y = 3.
False. The y-intercept is not provided, so this statement cannot be determined.
G) The line passes through the origin.
False. To check this, we can substitute (0, 0) into the equation. Let's use y = 2x - 6:
0 = 2(0) - 6
0 = -6 (False)
Since the equation does not hold for the origin, this statement is false.
H) The line passes through the point (1, -1).
True. To check this, we can substitute (1, -1) into the equation. Let's use y = 2x - 6:
-1 = 2(1) - 6
-1 = 2 - 6
-1 = -4 (False)
Since the equation does not hold for the given point, this statement is false.
Therefore, the three true statements are:
B) The gradient of the line is -3.
E) The equation of the line is y = 2x - 6.
H) The line passes through the point (1, -1).