write an equation in slope-intercept formfor the line passing through each pair of points.
(12,5) and (-4,1)
pleae help me!!!! i don't understanf how to solve it
first find the slope
slope =(5-1)/(12+4) = 4/16 = 1/4
so y = (1/4)x + b
but (-4,1) lies on it
so 1 = (1/4)(-4) + b
1 = -1+b
b = 2
equation: y = (1/4)x + 2
I usually check if the other point satisfies,
LS = 5
RS + (1/4)(12 + 2
= 3+2 = 5 = LS
my equation is correct
To find the equation of a line in slope-intercept form, you need to use the slope and one of the given points. The slope-intercept form of a line is given by the equation y = mx + b, where m represents the slope and b represents the y-intercept.
First, calculate the slope (m) using the given points (x1, y1) = (12, 5) and (x2, y2) = (-4, 1). The slope (m) is calculated as:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we have:
m = (1 - 5) / (-4 - 12)
m = -4 / -16
m = 1 / 4
Now that we have the slope (m), choose one of the given points (x1, y1), such as (12, 5). Substitute this point and the slope into the slope-intercept form equation (y = mx + b):
5 = (1/4)*12 + b
Next, solve for b by isolating it on one side of the equation:
5 = 3 + b
b = 5 - 3
b = 2
Finally, substitute the value of b back into the equation:
y = (1/4)x + 2
Therefore, the equation of the line passing through the points (12, 5) and (-4, 1) in slope-intercept form is y = (1/4)x + 2.