Question

A line passes through point (3, 7) and has a slope of 3/4.
The equation of the line is blank . If point A(x, 5) lies on the line, the value of x is blank .

Answer 1

y = mx + b
slope(m) = 3/4
(3,7)...x = 3 and y = 7
now sub
7 = 3/4(3) + b
7 = 9/4 + b
7 - 9/4 = b
28/4 - 9/4 = b
19/4 = b

so your equation is :
y = 3/4x + 19/4

Now we have points (x,5)....where y = 5. So we sub 5 in for y in our equation to find x
5 = 3/4x + 19/4
5 - 19/4 = 3/4x
20/4 - 19/4 = 3/4x --- multiply by 4 to get rid of fractions
20 - 19 = 3x
1 = 3x
1/3 = x

lets check..
y = 3/4x + 19/4
(1/3, 5)...x = 1/3 and y = 5
5 = 3/4(1/3) + 19/4
5 = 1/4 + 19/4
5 = 20/4
5 = 5 (correct)

points are (1/3, 5)