Question

What is the equation of the line that passes through the point (-2,5) and has a
slope of -4?

Answer 1

`\boxed {\boxed {\sf y= -4x -3}}`

Explanation:

We are asked to find the equation of a line given a point and the slope. We will use the point-slope formula.

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

In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of this line is -4 and the line passes through (-2,5).

• m= -4
• x₁= -2
• y₁ = 5

Substitute the values into the formula.

`y-5 = -4 (x--2)`

`y-5 = -4 (x+2)`

We are finding the equation of the line, so we should find the slope-intercept form or y=mx+b ( where m is the slope and b is the y-intercept).We must isolate the variable y on one side of the equation.

First, distribute the -4 on the right side of the equation. Multiply each term inside the parentheses by -4.

`y-5=( -4 *x ) + (-4* 2 )`

`y-5 =(-4x)+ (-8)\\y-5= -4x -8`

5 is being subtracted from y. The inverse operation of subtraction is addition, so we will add 5 to both sides of the equation.

`y-5 =-4x -8 + 5`

`y= -4x -3`

The equation of the line is y= -4x -3. The slope of the line is -4 and the y-intercept is -3.