The equation of the line that goes through the point ( 2, 5 ) and is parallel to the line going through the points ( -2 ,4 ) and ( 6 ,2 ) can be written in slope-intercept form y = mx+b with:
m =
b =
the slope is (2-4)/(6+2) = -1/4
So, in point-slope form, you have
y-5 = -1/4 (x-2)
Now massage that into slope-intercept form.
To find the equation of a line, we need to determine its slope (m) and y-intercept (b).
To find the slope (m), we can use the fact that the line we are looking for is parallel to the line passing through the points (-2,4) and (6,2).
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-2,4) and (6,2), we can substitute the values into the formula:
m = (2 - 4) / (6 - (-2))
= (-2) / 8
= -1/4
So, the slope (m) of the line we are looking for is -1/4.
Now, we can use the point-slope form of a line to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (2,5) and the slope we found (-1/4), we substitute the values into the equation:
y - 5 = (-1/4)(x - 2)
Next, we can simplify this equation and rewrite it in y = mx + b form by isolating y:
y - 5 = (-1/4)(x - 2)
y - 5 = (-1/4)x + 1/2
y = (-1/4)x + 1/2 + 5
y = (-1/4)x + 1/2 + 10/2
y = (-1/4)x + 11/2
Therefore, the equation of the line that goes through the point (2,5) and is parallel to the line passing through the points (-2,4) and (6,2) is y = (-1/4)x + 11/2, written in slope-intercept form.