Question

The points (-2, -10) and (4, r) lie on a line with slope 3. Find the missing coordinater.

Answer 1

To find the missing coordinate r for the point (4, r) on a line with slope 3, use the slope formula and the given point (-2, -10) resulting in r = 8.

Step-by-step explanation:

To find the missing coordinate r for the point (4, r) on the line with a slope of 3, one can use the slope formula m = (y2 - y1) / (x2 - x1), where m is the slope and (x1, y1) and (x2, y2) are the coordinates of two points on the line. Given the points (-2, -10) and (4, r), we substitute these values into the slope formula:

m = (r - (-10)) / (4 - (-2))

Since we know the slope, m, is 3, we can set up the equation:

3 = (r + 10) / 6

Multiplying both sides of the equation by 6 to clear the fraction gives us:

18 = r + 10

Now, subtracting 10 from both sides to isolate r:

r = 18 - 10

r = 8

Therefore, the missing coordinate r for the point (4, r) is 8.

Answer 2

Answer: 8

Step-by-step explanation:

(-2, -10) and (4, r)

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

⇒ 3 = (r -(-10)) ÷ (4 - (-2))

3 = (r + 10) ÷ (6)

18 = r + 10

∴ r = 8

Checking my answer:

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y + 10 = 3 (x + 2)

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer. The line passes through both the (-2, -10) point and (4, 8). So r = 8.