Question

Write the point-slope form of an equation of the line through the points (-7, 7) and (4, 1).

Answer 1

Answer:

Choice B. $\displaystyle y - 7 = -\frac{6}{11} \, (x + 7)$.

Step-by-step explanation:

Start by finding the slope of this line. Let $(x_1,\, y_1)$ and $(x_2,\, y_2)$ represent two distinct points on a line on a Cartesian Plane. (That is, $x_1 \ne x_2$.) The slope of this line would be:

$\displaystyle \frac{y_2 - y_1}{x_2 - x_1}$.

For the line in this question:

• $x_1 = -7$,
• $y_1 = 7$;

• $x_2 = 4,$
• $y_2 = 1$.

Indeed, $x_1 \ne x_2$. The slope of this line would thus be $\displaystyle \frac{1 - 7}{4 - (-7)}$, which is equal to $\displaystyle -\frac{6}{11}$.

On a Cartesian Plane, the point-slope form of a line that has a slope of $m$ and includes the point $(x_0,\, y_0)$ can be written as:

$y - y_0 = m\, (x - x_0)$.

(Note the minus signs in this form.)

For the line in this question, $m = \displaystyle -\frac{6}{11}$. There are two equivalent expressions for its point-slope form:

• Using the first point, $y - 7 = \displaystyle -\frac{6}{11}\, (x - (-7))$. This equation is equivalent to $y - 7 = \displaystyle -\frac{6}{11}\, (x + 7)$.
• Using the second point, $y - 1 = \displaystyle -\frac{6}{11}\, (x - 4)$.