Question

Which of the following is the equation of the line that is parallel to y=35x+8 y = 3 5 x + 8 and goes through point (-10,4)?

Answer 1

A parallel line to the equation y = 35x + 8 that passes through the point (-10, 4) would have the same slope of 35. Using the point-slope form, the equation is found to be y = 35x + 354.

Step-by-step explanation:

The original equation of the line provided is y = 35x + 8, which has a slope of 35. To find a line parallel to this line, we need a line with the same slope, because parallel lines have equal slopes. We also know that the new line must pass through the point (-10, 4).

To find the equation of this new line, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line goes through.

Substituting the given point and the slope we have:
y - 4 = 35(x + 10).
Simplifying the equation, we get:
y - 4 = 35x + 350
Adding 4 to both sides gives us the final equation:
y = 35x + 354.

Answer 2

Slope-intercept form of a line is y=mx+b.

Where m= slope and b= y-intercept.

First step is to compare the given equation y=35x+8 with the above equation to get the value of m.

After comparing the two equations we will get m=35.

Slope of paralle lines always equal which means slope of a line which is parallel to the above line will also be 35.

Now the line is passing through (-10,4).

Point slope form of a line is :

`y-y_(1) =m(x-x_(1) )`

Next step is to plug in m=35, x1=-10 and y1=4 in the above equation. So,

y-4=35(x-(-10)

y-4=35(x+10)

y-4=35x+350

y=35x+350+4

y=35x+354.

So, the equation of the line is y=35x+354.