(-5,3), (4,-5). Slope intercept form
you have two points. So, the line is
y-3 = (-5-3)/(4+5) (x+5)
now just rearrange that into y=mx+b form.
(-5,3), (4,-5).
Y = mx + b,
m = (-5-3)/(4-(-5)) = -8/9,
Y = (-8/9)(-5) + b = 3,
b = 3 - 40/9 = 27/9-40/9 = -13/9.
Eq: Y = (-8/9)x - 13/9.
To find the equation of a line in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to calculate the slope first using the given points (-5, 3) and (4, -5).
The slope (m) is given by the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let's substitute the values into the formula:
m = (-5 - 3) / (4 - (-5))
m = (-8) / (4 + 5)
m = -8 / 9
Now that we have the slope (m), we can proceed to find the equation of the line using the slope-intercept form.
Using one of the given points, for instance, (-5, 3), we can substitute the values into the equation:
y = mx + b
3 = (-8/9)(-5) + b
To solve for the y-intercept (b), we can simplify the equation:
3 = 40/9 + b
To isolate b, we subtract 40/9 from both sides:
b = 3 - 40/9
b = 27/9 - 40/9
b = -13/9
Now we have both the slope (m = -8/9) and the y-intercept (b = -13/9).
Therefore, the equation of the line in slope-intercept form is:
y = (-8/9)x - 13/9