Question

Write an equation of the line with the given slope that contains the given point.

Answer 1

`y-3=7(x-3)`

Explanation:

Pre-Solving

We are given that a line has a slope (m) of 7, and it contains the point A.

Point A has the coordinates of (3,3).

We want to write the equation of this line.

The equation of the line can be written in three different ways:

• Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
• Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be to 0, and a is usually non-negative.
• Point-slope form, which is
  `y-y_1=m(x-x_1)`, where m is the slope and
  `(x_1, y_1)` is a point.

Since the question does not specify that the equation had to be written in a specific way, any of these ways will work.

However, for the sake of this problem, let's write the equation in point-slope form, since it is the easiest.

Solving

Since we are already given the slope of this line, we can immediately plug it into
`y-y_1=m(x-x_1)`.

Replace m with 7.

`y-y_1=7(x-x_1)`

Let's label the values of the point A to avoid confusion / mistakes while calculating.

`x_1= 3\\y_1=3`

Substitute the values above into our equation.

`y-3=7(x-3)`

Answer 2

Answer : y = 7x - 18

The slope is given as 7

point A = (3, 3)

The slope - intercept form of equation

(y - y1) = m(x - x1)

x1 = 3, y1 = 3

(y - 3) = 7(x - 3)

Open the parentheses

y - 3 = 7*x - 7*3

y - 3 = 7x - 21

y = 7x - 21 + 3

y = 7x - 18

The equation of the line is y = 7x - 18