Question

Determine the equation of the line with slope m=−5 that contains the point (7,9).

a) y=−5x−22
b) y=−5x+22
c) y=5x+22
d) y=5x−22

Answer 1

The equation of the line with slope (m = -5) and passing through the point (7,9) is (y = -5x + 44) thus option B is correct.

Step-by-step explanation:

1. Point-Slope Form:

The equation of a line in point-slope form is
`\(y - y_1 = m(x - x_1)\),` where
`\((x_1, y_1)\)` is a point on the line, and \(m\) is the slope.

2. Substitute Values:

Substitute (m = -5), (
`x_1` = 7), and
`\(y_1 = 9\)` into the point-slope form:
`\(y - 9 = -5(x - 7)\).`

3. Simplify the Equation:

Expand and simplify the equation: (y - 9 = -5x + 35).

4. Isolate (y):

Isolate (y) by adding 9 to both sides: (y = -5x + 44).

5. Correct Answer:

The correct equation, therefore, is (y = -5x + 44), and the corresponding option is (b).

In summary, the equation is derived by substituting the given slope and point into the point-slope form and then simplifying to isolate (y). The correct answer is option (b), (y = -5x + 44).

Answer 2

The equation of the line with slope m = -5 that passes through the point (7,9) is:

a) y = -5x - 22

Step-by-step explanation:

To find the equation of a line with a given slope and a point it passes through, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point, m is the slope of the line. Given the slope m = -5 and the point (7,9), we substitute these values into the equation:

y - 9 = -5(x - 7)

Now, simplify and solve for y:

y - 9 = -5x + 35

y = -5x + 35 + 9

y = -5x + 44

Thus, the equation of the line in slope-intercept form (y = mx + b) is y = -5x + 44. This equation can be rearranged to match the format given in the choices by isolating the constant term on the other side of the equation:

y = -5x + 44

y = -5x - (-44)

y = -5x - 22

Hence, the correct choice for the equation of the line with slope m = -5 passing through the point (7,9) is y = -5x - 22.so the correct option is a.