Answer:
[tex]\boxed {\boxed {\sf y= -4x -3}}[/tex]
Step-by-step explanation:
We are asked to find the equation of a line given a point and the slope. We will use the point-slope formula.
[tex]y-y_1= m(x-x_1)[/tex]
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).
Substitute the values into the formula.
[tex]y-5 = -4 (x--2)[/tex]
[tex]y-5 = -4 (x+2)[/tex]
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.
[tex]y-5=( -4 *x ) + (-4* 2 )[/tex]
[tex]y-5 =(-4x)+ (-8)\\y-5= -4x -8[/tex]
5 is being subtracted from y. The inverse operation of subtraction is addition, so we will add 5 to both sides of the equation.
[tex]y-5 =-4x -8 + 5[/tex]
[tex]y= -4x -3[/tex]
The equation of the line is y= -4x -3. The slope of the line is -4 and the y-intercept is -3.
