Question

write the point - slope form of the lines equation satisfying the given conditions. then use the point - slope form of the equation to write the slope - intercept form of the equation. passing through (-2,8) and (6,8) what is the point - slope form of the equation of the line? (do not simplify. use integers or fractions for any numbers in the equation )

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(-2,8)$ and $(x_2,y_2)=(6,8)$. So, $m=\frac{8 - 8}{6-(-2)}=\frac{0}{8}=0$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-2,8)$ and $m = 0$, we get $y-8=0(x + 2)$. Using the point $(6,8)$ and $m = 0$, we also get $y - 8=0(x - 6)$.

Step3: Write the slope - intercept form

The slope - intercept form is $y=mx + b$. Since $m = 0$ and using the point $(-2,8)$ (substitute into $y=mx + b$: $8=0\times(-2)+b$, so $b = 8$), the equation is $y=0x+8$ or simply $y = 8$.

Answer:

Point - slope form: $y - 8=0(x + 2)$ or $y - 8=0(x - 6)$
Slope - intercept form: $y=8$