Answer:
3x + 4y = 7
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.