Question

Find an equation of the line having the given slope and containing the given point. m=-5 (5,7)

Answer 1

y - 7 = -5(x - 5)

Explanation:

Pre-Solving

We are given that a line has a slope of -5 and contains the point (5,7).

We want to write the equation of this line.

The equation of this line can be written in three ways:

• 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.
• Standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
• Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

Either one of these ways works, but let's use point-slope form, as that form is the easiest.

Solving

We can immediately substitute the values into the formula to get the equation.

We can start with the slope; replace m with -5 in the formula.

`y-y_1=m(x-x_1)` =>
`y-y_1=-5(x-x_1)`

Now, we can replace
`x_1` and
`y_1` with 5 and 7 respectively to get:

y - 7 = -5(x - 5)

Answer 2

y = -5x + 32

Explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write in known variables

slope m = -5

y = -5x + b

Step 2: Find b

7 = -5(5) + b

7 = -25 + b

b = 32

Step 3: Write linear equation

y = -5x + 32