Question

Write an equation in slope-intercept form that is perpendicular to (y=5x+3 and passes through the point (2,4)

- A. y=-15x+6
- B. y=-15x+2
- C. y=5x-14
- D. y=5x+6

Answer 1

The equation of a line perpendicular to y=5x+3 and passing through the point (2,4) would have a slope of -1/5. After using the point-slope form, the correct equation is y = (1/5)x + 22/5. Therefore, none of the provided options (A, B, C, D) is correct.

Step-by-step explanation:

To find the equation of a line that is perpendicular to y=5x+3 and passes through the point (2,4), we first need to identify the slope of the given line. The slope of the given line is 5. For a line to be perpendicular to this, its slope must be the negative reciprocal. The negative reciprocal of 5 is -1/5. Now we use the point-slope form to find the equation of the line that passes through (2,4) with a slope of -1/5:

y - y1 = m(x - x1)

Plugging in the values we have:

y - 4 = (-1/5)(x - 2)

Multiplying through by 5 to get rid of the fraction, we get:

5(y - 4) = -1(x - 2)

Distribute and simplify:

5y - 20 = -x + 2

Add 20 to both sides and x to both sides:

5y = x + 22

Divide everything by 5 to solve for y:

y = (1/5)x + 22/5

Therefore, the correct equation that is perpendicular to y=5x+3 and passes through the point (2,4) is not found among the options provided (A, B, C, D). None of the options match y = (1/5)x + 22/5.

Answer 2

The equation of a line perpendicular to y=5x+3 and passing through (2,4) would have a slope of -1/5 and y-intercept of 4.4, resulting in the equation y = -1/5x + 4.4. This does not match any of the answer choices provided.

Step-by-step explanation:

The question asks to write an equation in slope-intercept form that is perpendicular to the given line y=5x+3 and passes through the point (2,4). Since the original line has a slope of 5, the slope of the perpendicular line will be the negative reciprocal of 5, which is -1/5. To find the y-intercept (b), we use the point (2,4) and the new slope:

y - y1 = m(x - x1)

Plugging in the values we get:

4 - (-1/5)(2) = b

Which simplifies to:

4 + 2/5 = b

b = 4.4

Thus, the equation of the line is y = -1/5x + 4.4.

Looking at the answer choices, none of them match exactly with the derived equation, indicating there might be a mistake in the provided options, or an error in calculating the slope of the perpendicular line. If the slope of the original line had been misread and had actually been -1/5 (instead of 5), then the perpendicular slope would be 5, and option C, y = 5x - 14, is the one matching the correct slope. However, the y-intercept is incorrect as derived above.