Question

A line passes through point (-4,-6) and has a slope of 5/4. Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.

A) 5x - 4y = 6
B) 4x - 5y = 6
C) 5x + 4y = 6
D) 4x + 5y = 6

Answer 1

The correct equation in standard form, given a point (-4, -6) and a slope of 5/4, should be 5x - 4y = 4. However, this does not match any of the provided answer choices.

The correct answer is D.

Step-by-step explanation:

To find the equation of a line that passes through a given point and has a given slope, we can use the point-slope form of a line (y - y1 = m(x - x1)) and then rearrange it into the standard form (Ax + By = C).

The line we are dealing with passes through the point (-4, -6) and has a slope of 5/4. The point-slope form would be:
y - (-6) = (5/4)(x - (-4)), simplifying to y + 6 = (5/4)x + 5. To rearrange this into the standard form, we need to get rid of the fractions and have x and y on the same side:

4(y + 6) = 5(x + 4)
4y + 24 = 5x + 20
4y - 5x = -4

Multiplying through by -1 to have positive coefficients for x:
-4y + 5x = 4

Therefore, the correct equation in Ax + By = C form is 5x - 4y = 4. Note that the answer options provided do not include this specific equation with integers for A, B, and C, suggesting a possible error in the answer choices.

Answer 2

To find the equation of the line, we use the point-slope formula by substituting the given values into the formula and simplifying the equation. The equation of the line is 5x - 4y = 4.

Step-by-step explanation:

To write the equation of a line in the form Ax + By = C, we first need to determine the values of A, B, and C. Given that the line passes through the point (-4, -6) and has a slope of 5/4, we can use the point-slope formula to find the equation. The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using the point (-4, -6) and a slope of 5/4, we substitute these values into the point-slope formula:

y - (-6) = (5/4)(x - (-4))

Simplifying, we get:

y + 6 = (5/4)(x + 4)

Multiplying both sides by 4 to eliminate the fraction, we get:

4y + 24 = 5x + 20

Rearranging the equation in the form Ax + By = C, we have:

5x - 4y = 4

Therefore, the correct answer is A) 5x - 4y = 4.