Question

Which of the following is an equation of the line that passes through the point (5/3,-7) and has a slope of -3/4

Answer 1

The equation of the line is y = (-3/4)x - 13/4.

Step-by-step explanation:

To find the equation of the line that passes through the point (5/3,-7) and has a slope of -3/4, we can use the point-slope form of a linear equation: y - y1 = m(x - x1).

Plugging in the values (x1, y1) = (5/3, -7) and the slope m = -3/4, we get y - (-7) = (-3/4)(x - 5/3).

Simplifying the equation gives us y + 7 = (-3/4)x + 15/4.

Rearranging the equation to slope-intercept form, we have y = (-3/4)x + 15/4 - 7 = (-3/4)x - 13/4.

Answer 2

The slope form: y = mx + b

m = -3/4 therefore y = -3/4 x + b

The line passes trought the point (5/3, -7) → x = 5/3, y = -7.
Substitute the coordinates of the point to the equation:
-7 = -3/4 · 5/3 + b-
7 = -5/4 + b |+5/4
b = -28/4 + 5/4
b = -23/4

y = -3/4 x - 23/4 - the slope form

y = -3/4 x - 23/4 |· 44
y = -3x - 23 |+3x
3x + 4y = -23 - the strandard form