Question

Find an equation of the line that passes through the point (-1, 7) and is parallel to the line passing through the points (-3, -4) and (1, 4). (Let x be the independent variable and y be the dependent variable.)

Answer 1

To find a line parallel to another, determine the slope of the original line, which is 2 in this case, and then use the point-slope form with a given point and the same slope to find the equation, resulting in y = 2x + 9.

Step-by-step explanation:

To find an equation of the line that is parallel to another, we must first determine the slope of the given line. The line passing through the points (-3, -4) and (1, 4) has a slope calculated by the formula ∆y/∆x = (4 - (-4))/(1 - (-3)) = 8/4 = 2.

Since parallel lines have the same slope, our new line will also have a slope of 2. We can use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting our known point (-1, 7) and the slope 2, we get y - 7 = 2(x - (-1)). Simplified, the equation of our parallel line is y = 2x + 9.

Answer 2

Answer:
`y=2x+9`

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) =
`m=(d-b)/(c-a)`

⇒ Slope of line passing through (-3, -4) and (1, 4) =
`m=(4-(-4))/(1-(-3))`

`(4+4)/(1+3)=(8)/(4)=2`

i.e. Slope of line passing through (-3, -4) and (1, 4) = 2

We know that the slopes of two parallel lines are equal.

Therefore , the slope of line parallel to the line passing through the points (-3, -4) and (1, 4)= 2

Also, equation of line passing through point (a,b) and has slope m :

`(y-b)=m(x-a)`

Then, the equation of line passing through point (-1, 7) and has slope 2 :

`(y-7)=2(x-(-1))\\\\y-7=2(x+1)\\\\ y-7=2x+2\\\\ y=2x+2+7=2x+9\\\\ y=2x+9`

Hence, the required equation of the line that passes through the point (-1, 7) and is parallel to the line passing through the points (-3, -4) and (1, 4).

`y=2x+9`