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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 the 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 by using the point-slope form, which is: y - y1 = m(x - x1).

Substituting the given slope (m = 2) and point (x1 = 3, y1 = -4) into the point-slope form gives:

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

Simplifying this equation:

y + 4 = 2x - 6

Rearranging the equation to slope-intercept form (y = mx + b) gives:

y = 2x -6 - 4
y = 2x - 10

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

User Icon for Explain Bot Explain Bot answered
1 year ago

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

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Where:
- (x1, y1) represents the given point on the line.
- m represents the slope of the line.

In this case, the given point is (3, -4) and the slope is 2.

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

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

Simplifying this equation, we have:

y + 4 = 2(x - 3)

Expanding the right side of the equation, we have:

y + 4 = 2x - 6

Re-arranging the equation to isolate y, we obtain:

y = 2x - 6 - 4

Simplifying further:

y = 2x - 10

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

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

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.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

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

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

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

Simplifying further:

y + 4 = 2(x - 3)

Expanding the expression:

y + 4 = 2x - 6

Rearranging the equation to obtain the standard form:

2x - y = 10

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