Question

question
what is an equation of the line that passes through the points (2, 7) and (8, 4)?
answer attempt 1 out of 2

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(2, 7)$ and $(8, 4)$, we have $x_1 = 2$, $y_1 = 7$, $x_2 = 8$, $y_2 = 4$. So $m = \frac{4 - 7}{8 - 2} = \frac{-3}{6} = -\frac{1}{2}$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1 = m(x - x_1)$. Let's use the point $(2, 7)$. Substitute $m = -\frac{1}{2}$, $x_1 = 2$, and $y_1 = 7$ into the formula: $y - 7 = -\frac{1}{2}(x - 2)$.

Step3: Simplify to slope - intercept form

Expand the right - hand side: $y - 7 = -\frac{1}{2}x + 1$. Then add 7 to both sides: $y = -\frac{1}{2}x + 1 + 7$, so $y = -\frac{1}{2}x + 8$. We can also write it in standard form $x + 2y = 16$ (by multiplying both sides by 2: $2y = -x + 16$, then $x + 2y = 16$), but the slope - intercept form is also a valid equation of the line.

Answer:

$y = -\frac{1}{2}x + 8$ (or $x + 2y = 16$)