Question

Find an equation of the line with a slope of −7 that passes through the point (−3,12).

Answer 1

`\boxed {\boxed {\sf y=-7x-9}}`

Explanation:

Since we are given a point and the slope, we should use the point-slope formula.

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

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

We know the line passes through the point (-3, 12) and the slope is -7. Therefore,

• x₁= -3
• y₁= 12
• m= -7

Substitute the values into the formula.

`y-12=-7(x--3)`

Remember that 2 back to back negative signs become a positive.

`y-12=-7(x+3)`

Now we have to put the equation in slope-intercept form, or y=mx+b. Therefore, we need to isolate the variable y on one side of the equation.

First, distribute the -7. Multiply each term inside the parentheses by -7.

`y-12=(-7*x)+ (-7*3) \\y-12= (-7x)+(-21) \\y-12= -7x-21`

12 is being subtracted from y. The inverse operation of subtraction is addition. Add 12 to both sides of the equation.

`y-12+12=-7x-21+12\\y= -7x-21+12\\y=-7x-9`

The equation of the line is y=-7x-9