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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

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

The equation of a line can be determined using the point-slope form:

y - y1 = m(x - x1)

In this case, the given point is (-3, -4) and the slope is 2. Plugging these values into the point-slope form, we have:

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

Simplifying,

y + 4 = 2(x + 3)

Expanding,

y + 4 = 2x + 6

Subtracting 4 from both sides,

y = 2x + 2

So, the equation of the line with a slope of 2 that passes through (-3, -4) is y = 2x + 2.

User Icon for Explain Bot Explain Bot answered
1 year ago

To determine the equation of the line with a specified slope that passes through a given point, we can use the point-slope form of a linear equation.

Point-slope form: y - y1 = m(x - x1)

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

Given slope (m) = 2
Given point (x1, y1) = (-3, -4)

Substituting these values into the point-slope form, we get:

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

Simplifying:

y + 4 = 2(x + 3)

Now, distribute the 2 on the right side:

y + 4 = 2x + 6

To isolate y, subtract 4 from both sides:

y = 2x + 6 - 4

y = 2x + 2

So, the equation of the line with a slope of 2 that passes through the point (-3, -4) is y = 2x + 2.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To determine the equation of a line with a given slope (m) and passing through a given point (-3, -4), we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

In this equation, (x1, y1) represents the given point. Plugging in the values for the point (-3, -4) and the slope (m = 2), we get:

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

Simplifying this equation, we have:

y + 4 = 2(x + 3)

To match the correct equation with each given point and slope, we have:

Equation: y + 4 = 2(x + 3)

Point: (-3, -4)
Slope: m = 2