Question

Write the standard form of the equation of the line throught the given point with the given slope through: (1, 2), slope = 7​

Answer 1

`7x - y = 5`

Explanation:

The point-slope form of the equation of a line is:

`y - y_1 = m(x - x_1)`

where m is the slope and (x1, y1) is a point on the line.

You are given point (1, 2), so x1 = 1, and y1 = 2.

You are given slope = 7, so m = 7.

Plug in those values in the equation above.

`y - 2 = 7(x - 1)`

Now we change the equation to standard form.

Standard form of the equation of a line is:

ax + by = c

Distribute the 7.

`y - 2 = 7x - 7`

`-7x + y - 2 = -7`

`-7x + y = -5`

`7x - y = 5`

Answer 2

7x - y = 5

Explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Here m = 7, thus

y = 7x + c ← is the partial equation

To find c substitute (1, 2) into the partial equation

2 = 7 + c ⇒ c = 2 - 7 = - 5

y = 7x - 5 ← in slope- intercept form

Add 5 to both sides

y + 5 = 7x ( subtract y from both sides )

5 = 7x - y, that is

7x - y = 5 ← in standard form