Question

Write the equation of a line with a slope of 3 and passes through the point (-1,-8). Show steps please

Answer 1

y = 3x-5

Explanation:

`(-1,-8) = (x_1,y_1) \\ m = 3`

Substitute values into point slope form

`y - y_1 = m(x - x_1) \\ y - ( - 8)) = 3(x - ( - 1)) \\ y + 8 = 3(x + 1) \\ y + 8 = 3x + 3`

`y = 3x + 3 - 8 \\ y = 3x - 5`

Answer 2

y=3x-5

Explanation:

We are given a point and a slope, so we can use the point-slope formula.

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

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

The slope is 3 and the point given is (-1,-8). Therefore,

`m=3 \\x_(1) =-1\\y_(1)=-8`

Substitute the values into the formula.

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

`y--8=3(x- -1)`

Simplify the signs. Two negative signs become a positive sign.

`y+8=3(x+1)`

Distribute the 3. Multiply each term inside the parentheses by 3.

`y+8= (3*x)+(3*1)`

`y+8=3x+3`

We want to find the equation in slope-intercept form: y=mx+b. Therefore, we must isolate y. 8 is being added to y. The inverse of addition is subtraction. Subtract 8 from both sides.

`y+8-8=3x+3-8`

`y=3x+3-8`

`y=3x-5`

The equation of the line is y=3x-5 ⇒ m= 3, b= -5