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.

The correct equation for the line with slope 2 that passes through the point (-3, 4) is y = 2x + 10.

To determine the equation of a line, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) represents a point on the line, and m represents the slope of the line.

Let's start with the first point (-3, 4) and slope m = 2.
Substituting the values into the point-slope equation, we have:

y - 4 = 2(x - (-3))

Simplifying the equation, we get:

y - 4 = 2(x + 3)

To find the equation in the slope-intercept form (y = mx + b), we need to further simplify the equation. Distribute 2 to both terms inside the parentheses:

y - 4 = 2x + 6

Now, isolate y by adding 4 to both sides of the equation:

y = 2x + 10

Therefore, the equation of the line with the slope m = 2 passing through the point (-3, 4) is y = 2x + 10.

Now you can repeat the process for the other given points and slope to find the corresponding equations.

To determine the equation of a line given a point and slope, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Let's calculate the equations for each given point and slope:

For (–3, 4) with m = 2:
Substituting x1 = -3, y1 = 4, and m = 2 into the point-slope form, we get:
y - 4 = 2(x - (-3))
Simplifying:
y - 4 = 2(x + 3)
y - 4 = 2x + 6
y = 2x + 10

For (3, -4) with m = 2:
Substituting x1 = 3, y1 = -4, and m = 2 into the point-slope form, we get:
y - (-4) = 2(x - 3)
Simplifying:
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 10

For (–3, –4) with m = 2:
Substituting x1 = -3, y1 = -4, and m = 2 into the point-slope form, we get:
y - (-4) = 2(x - (-3))
Simplifying:
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

WHats the answer to all of them