Answer:
a) y = 2x - 4
b) y = -3x + 7
c) y = 5x - 3
Explanation:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]
where m = slope of the line
(x1, y1) = the coordinates of the given point
a) Given the slope(m) as 2 and the point (3, 2) where x1 = 3 and y1 = 2, we can write the equation of the line by substituting the given values into the point-slope form equation and solving for y as seen below;
[tex]\begin{gathered} y-2=2(x-3) \\ y-2=2x-6 \\ y=2x-6+2 \\ y=2x-4 \end{gathered}[/tex]
So the equation of the line can be written as y = 2x - 4
b) Given the slope(m) as -3 and the point (1, 4) where x1 = 1 and y1 = 4, we can write the equation of the line by substituting the given values into the point-slope form equation and solving for y as seen below;
[tex]\begin{gathered} y-4=-3(x-1) \\ y-4=-3x+3 \\ y=-3x+3+4 \\ y=-3x+7 \end{gathered}[/tex]
So the equation of the line is y = -3x + 7
c) Given the slope(m) as 5 and the point (1, 2) where x1 = 1 and y1 = 2, we can write the equation of the line by substituting the given values into the point-slope form equation and solving for y as seen below;
[tex]\begin{gathered} y-2=5(x-1) \\ y-2=5x-5 \\ y=5x-5+2 \\ y=5x-3 \end{gathered}[/tex]
So the equation of the line is y = 5x - 3
