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.
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(–3, 4) m = 2
(3, –4) m = 2
(–3, –4) m = 2
The equation of a line with a given slope (m) and passing through a given point (x₁, y₁) can be found using the point-slope form:
y - y₁ = m(x - x₁)
Let's calculate the equations for each given point and slope:
1) (–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
2) (3, –4) with m = 2:
Again, using the point-slope form, we have:
y - (-4) = 2(x - 3)
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 10
3) (–3, –4) with m = 2:
Once again, 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 correct equations for each given point and slope are:
(–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 a line with a specified slope that passes through a given point, 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.
Let's use this formula to determine the equations for each given point and slope:
1. (–3, 4) m = 2:
Using the point-slope form with (x1, y1) = (–3, 4) and m = 2:
y - 4 = 2(x - (-3))
Simplifying the equation:
y - 4 = 2(x + 3)
Expanding the brackets:
y - 4 = 2x + 6
Bringing all the terms to one side:
y - 2x - 10 = 0
So, the equation of the line with slope 2 that passes through (-3, 4) is y - 2x - 10 = 0.
2. (3, –4) m = 2:
Following the same steps as before, using (x1, y1) = (3, –4) and m = 2:
y - (-4) = 2(x - 3)
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y - 2x + 10 = 0
Therefore, the equation of the line with slope 2 that passes through (3, -4) is y - 2x + 10 = 0.
3. (–3, –4) m = 2:
Again, using the point-slope formula with (x1, y1) = (–3, –4) and m = 2:
y - (-4) = 2(x - (-3))
y + 4 = 2(x + 3)
y + 4 = 2x + 6
y - 2x + 2 = 0
Hence, the equation of the line with slope 2 that passes through (-3, -4) is y - 2x + 2 = 0.
To determine the equation of a line with a specified slope and passing through a given point, we can use the point-slope form of a line equation.
The point-slope form is given by:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) are the coordinates of the given point.
Let's solve each question step by step.
1) (–3, 4) m = 2
Using the point-slope form, we substitute the values:
y - 4 = 2(x - (-3))
Simplify:
y - 4 = 2(x + 3)
Expand the right side:
y - 4 = 2x + 6
Add 4 to both sides to isolate y:
y = 2x + 10
So, the equation of the line with a slope of 2 passing through the point (–3, 4) is y = 2x + 10.
2) (3, –4) m = 2
Using the point-slope form, we substitute the values:
y - (-4) = 2(x - 3)
Simplify:
y + 4 = 2(x - 3)
Expand the right side:
y + 4 = 2x - 6
Subtract 4 from both sides to isolate y:
y = 2x - 10
So, the equation of the line with a slope of 2 passing through the point (3, –4) is y = 2x - 10.
3) (–3, –4) m = 2
Using the point-slope form, we substitute the values:
y - (-4) = 2(x - (-3))
Simplify:
y + 4 = 2(x + 3)
Expand the right side:
y + 4 = 2x + 6
Subtract 4 from both sides to isolate y:
y = 2x + 2
So, the equation of the line with a slope of 2 passing through the point (–3, –4) is y = 2x + 2.