How do I find equation of the line that satisfies the given conditions

Question

Through (1,3); parallel to the line y=5x-1

Answer 1

The standard form for any linear equation is y = mx + b, where m is the slope and b the y-intercept.

What makes two lines parallel is the shared slope. So, our line is parallel to y = 5x - 1, where 5 is the slope, making the slope (m) of the line we are looking for also 5.

To find a line using one point on that line and the lines slop, you can use the point-slope form...

y - y₁ = m(x-x₁)

...where x₁ and y₁ are our x and y coordinates for the point on the line we are looking for.

We get...

y - 3 = 5(x - 1)

...and can solve.

y - 3 = 5(x - 1) | distribute parenthesis

y - 3 = 5x - 5 | +3

y = 5x - 2

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Answer 2

A line that is parallel to another has the same slope as that other line. So, to find the slope of the line in question, we just need to find the slope of y = 5x - 1. This line is in the slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept) so we can just look at the coefficient in front of the x to get the slope. the slope (m) is 5 so the slope of the line we are looking for is 5.

We now have the slope and a single point on the line (1, 3) so we can find the equation in a couple of ways. The easiest is to use the point-slope form of a line. It can be written as (y - y₁) = m(x - x₁) where m is the slope and a point on that line is the point (x₁, y₁). So, the equation of the line would be (y - 3) = 5(x - 1)

Answer 3

When a line is parallel to another line, their slopes are the same. Therefore, since the line you're looking for is parallel to the line y = 5x - 1, the line you're looking for has a slope of 5. (We know this because y = mx + b)

So our line has the point (1,3) and m = 5

We also have a myriad of equations to use to find the equation of a line (use your favorite one) I personally like:

y - y₁ = m(x - x₁)

Here (x₁, y₁) represent the point (1,3)

y - 3 = 5(x - 1)

y - 3 = 5x - 5

y = 5x - 2

Hope this helps

Mr. K

Answer 4

The coordinates given (1,3) showcase the x & y coordinates (x,y). To solve for the equation of the line that is parallel to the one given, we take the equation y=mx+b and plug in our x & y values (1,3). Since we want to find a line that is parallel to y=5x-1, we use a slope of 5, which is the value for "m". Therefor we use pemdas and algebra to solve for the missing variable:

y=mx+b

3=(5)(1)+b

3=5+b

-2=b

The equation of the line that if parallel to y=5x-1 and goes through the points (1,3) is:

y=5x-2