Answer:
Choice B. [tex]\displaystyle y - 7 = -\frac{6}{11} \, (x + 7)[/tex].
Step-by-step explanation:
Start by finding the slope of this line. Let [tex](x_1,\, y_1)[/tex] and [tex](x_2,\, y_2)[/tex] represent two distinct points on a line on a Cartesian Plane. (That is, [tex]x_1 \ne x_2[/tex].) The slope of this line would be:
[tex]\displaystyle \frac{y_2 - y_1}{x_2 - x_1}[/tex].
For the line in this question:
- [tex]x_1 = -7[/tex],
- [tex]y_1 = 7[/tex];
- [tex]x_2 = 4,[/tex]
- [tex]y_2 = 1[/tex].
Indeed, [tex]x_1 \ne x_2[/tex]. The slope of this line would thus be [tex]\displaystyle \frac{1 - 7}{4 - (-7)}[/tex], which is equal to [tex]\displaystyle -\frac{6}{11}[/tex].
On a Cartesian Plane, the point-slope form of a line that has a slope of [tex]m[/tex] and includes the point [tex](x_0,\, y_0)[/tex] can be written as:
[tex]y - y_0 = m\, (x - x_0)[/tex].
(Note the minus signs in this form.)
For the line in this question, [tex]m = \displaystyle -\frac{6}{11}[/tex]. There are two equivalent expressions for its point-slope form:
- Using the first point, [tex]y - 7 = \displaystyle -\frac{6}{11}\, (x - (-7))[/tex]. This equation is equivalent to [tex]y - 7 = \displaystyle -\frac{6}{11}\, (x + 7)[/tex].
- Using the second point, [tex]y - 1 = \displaystyle -\frac{6}{11}\, (x - 4)[/tex].
