What is the equation of the line that passes through (5,-2) and (-3,4)

3x + 4y = 7

Step-by-step explanation:

The slope = difference of y values / corresponding difference in x values of the 2 points.

Here it  is (4 - (-2) / (-3 - 5)

= 6 /-8 = -3/4.

Now we use the point/slope form of the equation of a line:

y - y1 = m(x - x1)  where m = slope and (x1, y1) is a point on the line.

We take the point (5, -2) and m = -3/4:

y - (-2) = -3/4 (x - 5)

y + 2 = -3/4x + 15/4

y = -3/4 x + 15/4 - 8/4

y = -3/4 x + 7/4  This is the equation in slope/intercept form.

To convert it to standard form we multiply through by 4 and rearrange:

4y = -3x + 7

3x + 4y = 7  is standard form.

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