Question

Find the equation of the line with slope −7 which goes through the point (−5,5).
Give your answer in slope-intercept form y=mx+b.

Answer 1

Answer:

$\boxed {\boxed {\sf y= -7x -30}}$

Step-by-step explanation:

We are asked to find the equation of a line,  given a point and a slope.

We can use the point-slope formula:

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

In this formula, (x₁, y₁) is the point and m is the slope. This line has a slope of -7 and passes through the point (-5,5). Therefore:

• x₁ = -5
• y₁= 5
• m= -7

Substitute the values into the formula.

$y-5= -7 (x- -5)$

$y-5= -7(x+5)$

We want to give the answer in slope-intercept form, or y=mx+b. We must isolate the variable y.

First, distribute the -7 on the right side of the equation. Multiply each term inside the parentheses by -7.

$y-5= (-7*x) + (-7*5)\\y-5 = (-7x) + (-35) \\y-5= -7x -35$

5 is being subtracted from y. The inverse operation of subtraction is addition. Add 5 to both sides of the equation.

$y-5+5 =-7x -35 +5 \\y= -7x -35 +5 \\y= -7x +30$

The equation of the line is y= -7x+30.