Write an equation of the line that passes through the given point and is parallel to the graph of the given equation.(2,-1); y=5x-2. (0,-5); y=9x

Question 1:


Find Slope

Equation: y = 5x - 2
Slope = 5
Slope of parallel line = 5


Insert slope into the general equation y = mx + c

y = 5x + c


Find y-intercept

At point (2, -1)
y = 5x + c
-1 = 5(2) + c
c = -1 - 10
c = -11


Insert y-intercept into the equation

y = 5x + c
y = 5x - 11


y = 5x - 11


Question 2:


Find Slope

y = 9x 
Slope = 9 
Slope of the parallel line = 9


Insert slope into the equation y = mx + c

y = 9x + c


Find y-intercept

y = 9x + c
At point (0, 5)
5 = 9(0) + c
c = 5


Insert y-intercept into the equation

y = 9x + c
y = 9x + 5


y = 9x + 5

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.