Question

Does the point (-4, 3) fall on the graph of this line? How do you know? Show your work. ( 2 points) PLEASE HELP ILL MARK BRAINLIEST

Answer 1

Answer:

Step-by-step explanation:

Since we know the line goes through points $(8,9)$ and $(2,4)$, we can construct a line in slope-intercept form

$y = mx + b$

where $m$ is the slope and $b$ is the Y-intercept.

The slope can be found using the two points provided:

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$\frac{9 - 4}{8 - 2}$

$\frac{5}{6}$

The line is now represented as

$y = \frac{5}{6}x + b$

To solve for $b$, we can plug in one of the two points:

$y = \frac{5}{6}x + b$

$(9) = \frac{5}{6}(8) + b$

$4 = \frac{20}{3} + b$

$b = \frac{-8}{3}$

We know have our line:

$y = \frac{5}{6}x - \frac{8}{3}$

To determine if the point $(-4, 3)$ falls on this line, we just plug the numbers into the equation and see if it holds true:

$y = \frac{5}{6}x - \frac{8}{3}$

$(3) = \frac{5}{6}(-4) - \frac{8}{3}$

$3 = \frac{-10}{3} - \frac{8}{3}$

$3 = \frac{-18}{3}$

$3 = -6$

This does not hold true, so the point is not on the line.