Answer:
[tex]y-9 = \frac{15}{7} (x-8)[/tex]
Step-by-step explanation:
Point-slope form is represented by [tex]y-y_1 = m (x-x_1)[/tex]. 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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line crosses, and [tex]x_2[/tex] and [tex]y_2[/tex] 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:
[tex]\frac{(9)-(-6)}{(8)-(1)} \\= \frac{9+6}{8-1} \\= \frac{15}{7}[/tex]
Thus, the slope is [tex]\frac{15}{7}[/tex].
2) Now, using the point-slope form of [tex]y-y_1 = m (x-x_1)[/tex], substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values in order to write an equation in point-slope form. The [tex]m[/tex] represents the slope, so substitute [tex]\frac{15}{7}[/tex] in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] 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 [tex]x_1[/tex] and [tex]y_1[/tex]. (I chose (8,9)). This gives the following equation and answer:
[tex]y-9 = \frac{15}{7} (x-8)[/tex]
