Question

PLS HELP


reposting this again pls help

Answer 1

4/3x + y = -14/3

Explanation:

Currently, the line we're given is in standard form, whose general form is

`Ax+By=C`

We will need to find the slope of this line, since the slopes of perpendicular lines are negative reciprocals. This is shown by the formula:

`m_(2)=-1/m_(1)`, where m2 is the slope of the line we're trying to find and m1 is the slope of the line we're given.

Furthermore, we can find the slope of the line by converting the line from standard form to slope-intercept form, whose general form is

`y=mx+b`, where m is the slope and b is the y intercept:

`3/4x-y=7/2\\-y=-3/4x+7/2\\y=3/4x-7/2`

Now, if we allow 3/4 to be m2 in the formula I provided, we can find the slope of the other line:

`m_(2)=-1/(3/4)\\ m_(2)=-4/3`

Now, that we've found the slope of the new line, we can find the y-intercept by plugging in the slope and the point (-2, -2) for x and y in the slope-intercept form:

`-2=-4/3(-2)+b\\-2=8/3+b\\-14/3=b`

Thus, the equation of the line passing through (-2, -2) and perpendicular to 3/4x - y = 7/2 is y = -4/3x - 14/3

In order to clear up confusion, we can convert this line to standard form so that it truly resembles the other line by simply isolating -14/3 (b in the slope-intercept form):

`y=-4/3x-14/3\\4/3x+y=-14/3`