Question

write the equation of a line that is parallel to the line y=3x+5 and goes through the point (9,1)​

Answer 1

Answer:

Step-by-step explanation:

y = 3x + 5

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 5 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, thus

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (- 1, 2) into the partial equation

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = 3x + 5 ← equation of parallel line

Answer 2

Answer:

y=3x-26

Step-by-step explanation:

Hi there!

We are given the line y=3x+5, and we want to write an equation that is parallel to that line, and goes through the point (9, 1)

Parallel lines have the same slope; so let's find the slope of y=3x+5

The line is written in the format y=mx+b, where m is the slope and b is the y intercept

Since 3 is in the place of where m is in the equation, the slope of the line is 3.

Because we are given the point (9,1) and the slope 3, we can write the equation using point-slope form, which is $y-y_1=m(x-x_1)$, where m is the slope and $(x_1, y_1)$ is a point

We have everything we need to write the equation in point-slope form, let's just label their values to avoid any confusion:

m=3

$x_1=9\\y_1=1$

Substitute these values into the formula above:

$y-y_1=m(x-x_1)$

y-1=3(x-9)

The equation can be left as that, or you can re-write it into slope-intercept form (y=mx+b form) if you wish

In order to do that, we first need to open up the parentheses by multiplying x and -9 by 3:

y-1=3x-27

Add 1 to both sides

y=3x-26

Hope this helps!