write the equation of the line that passes through the points (7, -4) and (-1, 3), first in point - slope…

Explanation:

Step1: Calculate the slope

The slope $m$ formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(7,-4)$ and $(x_2,y_2)=(-1,3)$. So $m=\frac{3-(-4)}{-1 - 7}=\frac{3 + 4}{-8}=-\frac{7}{8}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(7,-4)$ and $m =-\frac{7}{8}$, we get $y-(-4)=-\frac{7}{8}(x - 7)$, which simplifies to $y + 4=-\frac{7}{8}(x - 7)$.

Step3: Convert to slope - intercept form

Start with $y + 4=-\frac{7}{8}(x - 7)$. Expand the right side: $y+4=-\frac{7}{8}x+\frac{49}{8}$. Then subtract 4 from both sides: $y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}$, so $y=-\frac{7}{8}x+\frac{17}{8}$.

Answer:

The slope of the line is $-\frac{7}{8}$. When the point $(7,-4)$ is used, the point - slope form of the line is $y + 4=-\frac{7}{8}(x - 7)$. The slope - intercept form of the line is $y=-\frac{7}{8}x+\frac{17}{8}$.