Question

Write the equation of a line that passes through the points (-3, 7) and (3, 3).

Answer 1

Answer:

y = -2/3x + 5

Step-by-step explanation:

(-3, 7) and (3, 3)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(3 - 7) / (3 -(-3))

Simplify the parentheses.

= (3 - 7) / (3 + 3)

Simplify the fraction.

= (-4) / (6)

= -4/6

= -2/3

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = -2/3x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (3, 3). Plug in the x and y values into the x and y of the standard equation.

3 = -2/3(3) + b

To find b, multiply the slope and the input of x(3)

3 = -2 + b

Now, add 2 to both sides to isolate b.

5 = b

Plug this into your standard equation.

y = -2/3x + 5

This is your equation.

Check this by plugging in the other point you have not checked yet (-3, 7).

y = -2/3x + 5

7= -2/3(-3) + 5

7 = 2 + 5

7 = 7

Your equation is correct.

Hope this helps!