Plz, . will give ! 40 find the equation of a line through (4, -3) that is parallel to the line that passes through these points (-4,7) and (2,4). write your answer in standard form (ax + by = c). show all your work.

x + 2y = -2

Step-by-step explanation:

First, find the slope of the line that passes through (-4,7) and (2,4).  As we move to the right from -4 to 2, x increases by 6, and y decreases by 3.

Thus, the slope of this given line is m = rise / run = -3/6, or -1/2.

Then a new line which is parallel to the given one must have the same slope:  -1/2.

Starting with the slope-intercept form y = mx + b, we find the equation of the line through (4, -3) that is parallel to the line we just studied (above).

y = mx + b becomes -3 = (-1/2)(4) + b,  or  -3 = -2 + b.  Then b = -1:  

y = (-1/2)x - 1.  We must put this into the form (Ax + By = C).

Multiply all terms of y = (-1/2)x - 1 by 2 to eliminate the fractional coefficient:

2y = -x - 2.  Moving -x to the left side, we get:

x + 2y = -2

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the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (:

answer: 59

step-by-step explanation: