Question

(-7 -3) (-3, 5) write an equation of a line that passes through each pair of points

Answer 1

To write an equation of a line that passes through two points, use the slope-intercept form. Find the slope using the formula and substitute the values into the equation.

Step-by-step explanation:

To write an equation of a line that passes through two points, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Given the points (-7, -3) and (-3, 5), we can find the slope by using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (5 - (-3)) / (-3 - (-7)) = 8 / 4 = 2.

Now that we have the slope, we can choose either point and substitute the values into the equation. Let's use the first point (-7, -3): -3 = 2(-7) + b. Solving for b, we get b = -3 - 2(-7) = -3 + 14 = 11.

Therefore, the equation of the line that passes through the points (-7, -3) and (-3, 5) is y = 2x + 11.

Answer 2

y = 2x + 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, - 3) and (x₂, y₂ ) = (- 3, 5)

m =
`(5+3)/(-3+7)` =
`(8)/(4)` = 2, thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using (- 3, 5 ), then

5 = - 6 + c ⇒ c = 5 + 6 = 11

y = 2x + 11 ← equation of line