the slope intercept form of the equation of a straight line is y = mx + b.
m is the slope
b is the y-intercept.
the line parallel to y = 2x - 6 will have the same slope.
therefore the slope intercept form of the equation of the line parallel to y = 2x - 6 will be y = 2x + b.
you only need to find the value of b.
you want the line to have the same x-intercept as the line defined by 14x + 7y - 14 = 0
convert this equation to slope intercept form as follows:
start with 14x + 7y - 14 = 0
subtract 14x from both sides of the equation and add 14 to both sides of the equation to get 7y = -14x + 14
divide both sides by 7 to get y = -2x + 2
to find the x-intercept of that line, set y = 0 to get:
0 = -2x + 2
add 2x to both sides of that equation to get 2x = 2
divide both sides of that equation to get x = 1
the x-intercept of that equation is x = 1.
that's the value of x when the value of y is equal to 0.
you want the same x-intercept for the line parallel to y = 2x - 6
that line is y = 2x + b
the x-intercept is the value of x when y is equal to 0.
you were given that as x = 1.
set y equal to 0 and x equal to 1 and y = 2x + b becomes 0 = 2 + b
solve for b to get b = -2
the equation of that line becomes y = 2x - 2
y = 2x - 2 is parallel to y = 2x - 6 because it has the same slope and a different y-intercept.
to see if we did good, graph all 3 equations as shown below.
y = 2x - 6 is red.
the line parallel to it (y = 2x - 2) is orange.
the line that has the same x-intercept as the line parallel to y = 2x - 6 is in blue.
the orange line is y = 2x - 2
it is parallel to y = 2x - 6
it also has the same x-intercept as y = -2x + 2
just look at the orange line and you'll see what i mean.
the y-intercept is at y = -2.
that's the value of y when x is equal to 0.
the x-intercept is at x = 1
that's the value of x when y is equal to 0.
there are two equations in blue.
they are y = -2x + 2 and 14x + 7y - 14 = 0.
they generate the same line because they're equivalent.
y = -2x + 2 is the slope intercept form of 14x + 7y - 14 = 0.
let me know if you have any questions.
theo