Find an equation of the line that satisfies the given conditions.

Through (5, 3) and (4, 7)

slope = (7-3)/(4-5) = -4

using the point (5,3)
y - 3 = -4(x - 5)

dress it up any way you want to

To find the equation of a line, we can use the slope-intercept form of the equation, which is:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

First, let's find the slope (m) using the coordinates of the two given points.

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (5, 3) and (4, 7):

m = (7 - 3) / (4 - 5)
m = 4 / -1
m = -4

Now that we have the slope (m), we can proceed to find the y-intercept (b) by substituting the values of one of the points (let's use (5, 3)) into the slope-intercept form:

y = mx + b
3 = -4(5) + b

Now, solve for b:

3 = -20 + b
b = 3 + 20
b = 23

Therefore, the equation of the line that satisfies the given conditions is:

y = -4x + 23