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

n o 987654345678876434yu4567765

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

i do not know the answer

step-by-step explanation: