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) with m=2 - y = 2x + 10
(3, -4) with m=2 - y = 2x - 10
(-3,-4) with m=2 - y = 2x + 2
To determine the equation of the line with the specified slope that passes through the given point, we can use the point-slope form of a linear equation, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Let's match the correct equation with each given point and slope:
1. For (-3, 4) with m = 2:
Using the point-slope form, we have:
y - 4 = 2(x - (-3))
y - 4 = 2(x + 3)
y - 4 = 2x + 6
y = 2x + 10
Therefore, the equation of the line with a slope of 2 passing through (-3, 4) is y = 2x + 10.
2. For (3, -4) with m = 2:
Using the point-slope form, we have:
y - (-4) = 2(x - 3)
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 10
Therefore, the equation of the line with a slope of 2 passing through (3, -4) is y = 2x - 10.
3. For (-3, -4) with m = 2:
Using the point-slope form, we have:
y - (-4) = 2(x - (-3))
y + 4 = 2(x + 3)
y + 4 = 2x + 6
y = 2x + 2
Therefore, the equation of the line with a slope of 2 passing through (-3, -4) is y = 2x + 2.
Matching the equations with the given points and slopes, we have:
(-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 passing through a given point, we can use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) are the coordinates of the given point.
Let's start with the given points and slope:
1. (-3, 4) with m = 2:
Using the point-slope form, we substitute the values into the equation: y - 4 = 2(x - (-3)). Simplifying, we have y - 4 = 2(x + 3). Expanding and rearranging, we get y - 4 = 2x + 6. Finally, adding 4 to both sides gives y = 2x + 10. Therefore, the equation for this point and slope is y = 2x + 10.
2. (3, -4) with m = 2:
Again, using the point-slope form, we substitute the values: y - (-4) = 2(x - 3). Simplifying, we have y + 4 = 2(x - 3). Expanding and rearranging, we get y + 4 = 2x - 6. By subtracting 4 from both sides, we get y = 2x - 10. Thus, the equation for this point and slope is y = 2x - 10.
3. (-3, -4) with m = 2:
Once more, we use the point-slope form: y - (-4) = 2(x - (-3)), which simplifies to y + 4 = 2(x + 3). Expanding and rearranging, we have y + 4 = 2x + 6. Subtracting 4 from both sides gives y = 2x + 2. Hence, the equation for this point and slope is y = 2x + 2.
Matching the correct equations with each given point and slope:
(-3, 4) m = 2 - y = 2x + 10
(3, -4) m = 2 - y = 2x - 10
(-3, -4) m = 2 - y = 2x + 2