Determine the equation of the line with the specified slope that passes through the given point.
Match the correct equation with each given point and slope.
(-3, 4) m = 2 - _
(3,-4) m=2 - _
(-3, -4) m=2 - _
Word bank
y = 2x - 2
y = 2x -10
y = 2x + 2
y = 2x +10
(-3, 4) m = 2 -> y = 2x + 10
(3,-4) m = 2 -> y = 2x - 10
(-3, -4) m = 2 -> y = 2x + 2
To determine the equation of the line with the specified slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
1. For the point (-3, 4) and m = 2, the equation becomes:
y - 4 = 2(x - (-3))
y - 4 = 2(x + 3)
y - 4 = 2x + 6
Rearranging the equation, we get:
y = 2x + 6 + 4
y = 2x + 10
So, the equation is y = 2x + 10.
2. For the point (3, -4) and m = 2, the equation becomes:
y - (-4) = 2(x - 3)
y + 4 = 2(x - 3)
y + 4 = 2x - 6
Rearranging the equation, we get:
y = 2x - 6 - 4
y = 2x - 10
So, the equation is y = 2x - 10.
3. For the point (-3, -4) and m = 2, the equation becomes:
y - (-4) = 2(x - (-3))
y + 4 = 2(x + 3)
y + 4 = 2x + 6
Rearranging the equation, we get:
y = 2x + 6 - 4
y = 2x + 2
So, the equation is y = 2x + 2.
Matching the equations to the given points and slopes:
(-3, 4) m = 2: y = 2x + 10
(3, -4) m = 2: y = 2x - 10
(-3, -4) m = 2: y = 2x + 2
To determine the equation of a line with a specified slope that passes through a given point, we can use the point-slope formula:
y - y1 = m(x - x1)
where (x1, y1) represents the given point coordinates and m represents the slope.
Let's fill in the information for each case:
1. For the point (-3, 4) and slope m = 2:
Using the point-slope formula, we have:
y - 4 = 2(x - (-3))
y - 4 = 2(x + 3)
y - 4 = 2x + 6
y = 2x + 6 + 4
y = 2x + 10
So, the equation for this case is y = 2x + 10.
2. For the point (3, -4) and slope m = 2:
Using the point-slope formula, we have:
y - (-4) = 2(x - 3)
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 6 - 4
y = 2x - 10
Therefore, the equation for this case is y = 2x - 10.
3. For the point (-3, -4) and slope m = 2:
Using the point-slope formula, we have:
y - (-4) = 2(x - (-3))
y + 4 = 2(x + 3)
y + 4 = 2x + 6
y = 2x + 6 - 4
y = 2x + 2
Thus, the equation for this case is y = 2x + 2.
Matching each equation with its given point and slope:
- For (-3, 4) and m = 2: y = 2x + 10.
- For (3, -4) and m = 2: y = 2x - 10.
- For (-3, -4) and m = 2: y = 2x + 2.
So, the correct equation matches are:
- (-3, 4) with y = 2x + 10.
- (3, -4) with y = 2x - 10.
- (-3, -4) with y = 2x + 2.