Question

Write the equation of the line that passes through the points (1, -6) and (8, 9). Put

Answer 1

Answer:

$y-9 = \frac{15}{7} (x-8)$

Step-by-step explanation:

Point-slope form is represented by $y-y_1 = m (x-x_1)$. To write an equation with it, we need the slope of the line and a point the line crosses through. We already have at least one point the line crosses through, so let's figure out the slope.

To find the slope, use the slope formula $\frac{y_2-y_1}{x_2-x_1}$. $x_1$ and $y_1$ represent the x and y values of one point the line crosses, and $x_2$ and $y_2$ represent the x and y values of another point the line crosses. So, using the x and y values of (1, -6) and (8, 9), substitute them into the formula and solve:

$\frac{(9)-(-6)}{(8)-(1)} \\= \frac{9+6}{8-1} \\= \frac{15}{7}$

Thus, the slope is $\frac{15}{7}$.

2) Now, using the point-slope form of  $y-y_1 = m (x-x_1)$,  substitute $m$, $x_1$, and $y_1$ for real values in order to write an equation in point-slope form. The $m$ represents the slope, so substitute $\frac{15}{7}$ in its place. The $x_1$ and $y_1$ represent the x and y values of one point on the line. So, choose any one of the points given - either one is fine - and substitute its x and y values for $x_1$ and $y_1$. (I chose (8,9)). This gives the following equation and answer:

$y-9 = \frac{15}{7} (x-8)$