Answer:
[tex]y = \frac{4}{3}x - 13[/tex]
Step-by-step explanation:
The equation for a line in slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept. This means that the slope of [tex]y = \frac{4}{3}x + 5[/tex] is 4/3.
We would like to find a line parallel to [tex]y = \frac{4}{3}x + 5[/tex] which passes through the point (12, 3). Any parallel line must have the same slope, so the equation for the new line will be [tex]y = \frac{4}{3}x + b[/tex] for some number [tex]b[/tex]. We know that [tex]y[/tex] must be equal to 3 when [tex]x[/tex] is equal to 12, so 3 = (4/3)(12) + b. This means that 3 = 16 + b, so b = -13.
Therefore, the equation for the parallel line is [tex]y = \frac{4}{3}x - 13[/tex].
