Answer: The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
To find the equation of the line that passes through the points (-3, -1) and (2, 9), we can use the point-slope form with one of the points as (x1, y1) and use the slope formula to find the value of m:
m = (y2 - y1) / (x2 - x1)
Plugging in the values from the problem, we get:
m = (9 - (-1)) / (2 - (-3))
m = 10 / 5
m = 2
Now that we have the value of m, we can use the point-slope form with one of the points as (x1, y1) to find the equation of the line:
y - (-1) = 2(x - (-3))
y + 1 = 2(x + 3)
Therefore, the equation in point-slope form of the line that pas
Answer:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given points:
Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point (-3, -1) into the point-slope formula:
[tex]\implies y-(-1)=2(x-(-3))[/tex]
[tex]\implies y+1=2(x+3)[/tex]
Substitute the found slope and point (2, 9) into the point-slope formula:
[tex]\implies y-9=2(x-2)[/tex]
Therefore, the correct answer option is:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
