please help!!
Choose the equation below that represents the line passing through the point (−5, 1) with a slope of 3/2
A: y − 5 = 3/2 (x + 1)
B: y + 1 =3/2 (x − 5)
C: y + 5 = 3/2 (x − 1)
D: y − 1 = 3/2 (x + 5)
for a given point (p,q) and slope m
the equation is
y - q = m(x - p)
Which of the choices matches this pattern for your given data
To find the equation of a line passing through a given point with a given slope, you 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 coordinates of the given point, and m represents the slope.
In this case, the point given is (-5, 1) and the slope is 3/2.
To determine the correct equation from the given options, we need to substitute these values into the point-slope form and check which equation satisfies the condition.
Let's try each option:
A: y − 5 = 3/2 (x + 1)
Substituting the point (-5, 1) into the equation:
1 - 5 = 3/2 (-5 + 1)
-4 = 3/2 (-4)
-4 = -6
This equation does not hold, so Option A is not correct.
B: y + 1 =3/2 (x − 5)
Substituting the point (-5, 1) into the equation:
1 + 1 = 3/2 (-5 - 5)
2 = 3/2 (-10)
2 = -15
This equation does not hold, so Option B is not correct.
C: y + 5 = 3/2 (x − 1)
Substituting the point (-5, 1) into the equation:
1 + 5 = 3/2 (-5 - 1)
6 = 3/2 (-6)
6 = -9
This equation does not hold, so Option C is not correct.
D: y − 1 = 3/2 (x + 5)
Substituting the point (-5, 1) into the equation:
1 - 1 = 3/2 (-5 + 5)
0 = 3/2 (0)
0 = 0
This equation holds, so Option D is correct.
Therefore, the equation that represents the line passing through the point (-5, 1) with a slope of 3/2 is y − 1 = 3/2 (x + 5). Option D is the correct choice.