Find the equation of a line parallel to y=3x+2 that contains the point (2,−5). Write the equation in slope-intercept form.

y = 3x - 11

Step-by-step explanation:

First, let's find the slope of the line

y=3x+2

As the equation is already in slope-intercept form y=mx+c ,

Slope = 3

Let a point

(x,y) be on the new line.

By finding the slope again,

y+5/ x−2=3

y+5=3(x−2)

y+5=3x−6

Slope-intercept form:

y=3x−11

y = 3x -11

Step-by-step explanation:

First, rewrite the equation in standard form (Ax + By = C)

y=3x+2

3x - y = -2

To find the slope (m) of this line, it is equal to - A /B.

m = - 3 / -1

= 3

Parallel lines have equal slopes, so the new line also has a slope of 3.

Using point-slope form y-y1 = m(x-x1) ,

we can find the equation of the line.

y - (-5) = 3 ( x- 2)

y + 5 = 3x - 6

3x - y = 11

Slope-intercept form is y = mx + c

c is the y-intercept, which we have yet to find.

In y-intercept, x must be 0.

3(0) - y =11

y = -11

Therefore, the equation required will be:

y = 3x -11

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>