First, we need to determine the slope of the line. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(-5) - color(blue)(-8))/(color(red)(2) - color(blue)(3/4)) = (color(red)(-5) + color(blue)(8))/(color(red)(8/4) - color(blue)(3/4)) = 3/(5/4) = 12/5m=−5−−82−34=−5+884−34=354=125
Now, we can use the point-slope formula to write an equation for the line. The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))(y−y1)=m(x−x1)
Where color(blue)(m)m is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
Substituting the slope we calculated and the second point gives:
(y - color(red)(-5)) = color(blue)(12/5)(x - color(red)(2))
(y + color(red)(5)) = color(blue)(12/5)(x - color(red)(2))
We can also substitute the slope we calculated and the first point giving:
(y - color(red)(-8)) = color(blue)(12/5)(x - color(red)(3/4))
(y + color(red)(8)) = color(blue)(12/5)(x - color(red)(3/4))
We can also solve the first equation for y to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: y = color(red)(m)x + color(blue)(b)
Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.
y + color(red)(5) = (color(blue)(12/5) xx x) - (color(blue)(12/5) xx color(red)(2))
y + color(red)(5) = 12/5x - 24/5
y + color(red)(5) - 5 = 12/5x - 24/5 - 5
y + 0 = 12/5x - 24/5 - 25/5
y = color(red)(12/5)x - color(blue)(49/5)
