Question

find the equation of the line that passes through (3,1) and is parallel to y = 2 x + 3 leave your answer in the form y = m x + c

Answer 1

Step-by-step explanation:

How do I find the equation of the line y=mx + C, passing through the points M (-2, -3) and T (3, 7)?

How do I find the equation of the line y=mx + C, passing through the points M (-2, -3) and T (3, 7)?

A2A

y = mx + C is often called slope-intercept form.

There are two pieces of information you will need to solve for. #1: The slope, which is m, and #2: the y-intercept, which is C (incidentally I learned this as y = mx + b, instead of y = mx + C, but that is a trivial detail)

Step #1 Find the slope. use the formula slope = (y₂ - y₁)/(x₂ - x₁) => (7 - -3)/3 - -2) = 10/5 = 2. m=2

Step #2 Find the y-intercept. Solve for y = mx + C when x is 2 and x = -2 and y = -3 -3 = 2(-2) + C => -3 = -4 + C add 4 to both sides, 1 = C

Equation: y = 2x + 1.

Check: x = 3 => y = 2(3) + 1 => y = 6 + 1 => y = 7 => (3, 7)

Check: x = -2 => y = 2(-2) + 1 => y = -4 + 1 => y = -3 => (-2, -3)

Answer 2

Given :

1. line is passing through point (3,1)
2. line is parallel to the line $y=2x+3,,,,(2)$

to find : the equation of line in the form of y = mx + c

solution :

as we all know ,

general equation of line y = mx + c ..... (2)

where ,  m = slope of  line

$m1 = m2 ,$  if lines are parallel

=> m1 = m2 = 2

=> the equation of line is $y=2x+c.....(3)$

as the line passes through the point (3,1) the point satisfy the equation (3)

on putting the value of x and y in equation (3) we get

$1=2*3+c\\c=1-6=-5$

Hence, the equation of line is y = 2x - 5

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