Write the following equation -x+5y=3 in slope-intercept form is y = 1/5x + 3/5.
-x + 5y = 3;
5y = x + 3;
y = 1/5x + 3/5

y - y1 = m(x - x1),
m = (y2 - y1) / (x2 - x1),
m = (-9 - (-4)) / (-2 - 6)
m = (-9 + 4) / (-2 - 6)
m = -5 / -8
m = 5/8
y - (-4) = (5/8)(x - 6)
y + 4 = (5/8)(x - 6)
Y + 4 = (5/8)x - 15/4
y = (5/8)x - 15/4 - 4
y = (5/8)x - 15/4 - 16/4

Simplifying the expression:

y = (5/8)x - 31/4

Therefore, the equation for the line passing through the points (6, -4) and (-2, -9) is y = (5/8)x - 31/4.

Using the point-slope form, we substitute the slope (m = 4) and the coordinates (x1 = 3, y1 = -5) into the equation:

y - y1 = m(x - x1)

y - (-5) = 4(x - 3)

y + 5 = 4(x - 3)

y + 5 = 4x - 12

y = 4x - 12 - 5
y = 4x - 17

Therefore, the equation for the line that is parallel to y = 4x + 6 and passes through the point (3, -5) is y = 4x - 17.

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