Are these Correct?

Write an equation for the line in point/slope form and slope/intercept form that has the given condition.

1. Passes through (3, 2) and is parallel to 2x-y=4
= 4x+y

2. Passes through (-1, -1) and is perpendicular to y = 5/2x + 3
=6\7x-2

I can't interpret your answers.

1.
2x-y=4, or
y = 2x-4
has slope 2. So, the line through (3,2) with slope=2 is

y-2 = 2(x-3)
y = 2x-4

2.
y = 5/2 x + 3
has slope 5/2
so, the perpendicular line has slope -2/5

y+1 = -2/5 (x+1)
y = -2/5 x - 7/5

I'd be interested to know what steps you followed to arrive at your answers.

To determine if the equations you provided are correct, we can use the given conditions and properties of parallel and perpendicular lines.

1. For a line to be parallel to another line, they must have the same slope. The given line, 2x - y = 4, can be rewritten in slope-intercept form as y = 2x - 4. The slope of this line is 2. To find an equation in point-slope form, we can use the formula y - y1 = m(x - x1), where (x1, y1) is the given point (3, 2). Plugging in the values, we get y - 2 = 2(x - 3), which simplifies to y - 2 = 2x - 6. Finally, rearranging the equation, we have y = 2x - 4, which matches the given equation. Therefore, your equation is correct.

2. To find a line that is perpendicular to a given line, we need to determine its slope, which will be the negative reciprocal of the slope of the given line. The given line, y = (5/2)x + 3, has a slope of 5/2. The negative reciprocal of 5/2 is -2/5. Using the point-slope form, we have y - (-1) = (-2/5)(x - (-1)). Simplifying this equation gives y + 1 = (-2/5)(x + 1), which further simplifies to y + 1 = (-2/5)x - 2/5. Rearranging the equation, we have y = (-2/5)x - 2/5 - 1, which simplifies to y = (-2/5)x - 7/5. Therefore, your equation is not correct. The correct equation for a line passing through (-1, -1) and perpendicular to y = (5/2)x + 3 is y = (-2/5)x - 7/5.

In summary, equation 1 is correct, but equation 2 is not. The correct equation for the second condition is y = (-2/5)x - 7/5.