Slope-intercept form is y = mx + b
[m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]
To find the slope, use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] Plug in the two points into the equation
(2, 1) ---> (x₁, y₁)
(0, 2) ---> (x₂, y₂)
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-1}{0-2}[/tex]
[tex]m=-\frac{1}{2}[/tex] Now that you have the slope, plug it in:
y = mx + b
y = -1/2x + b To find b, plug in one of the points. I will use (0, 2)
2 = -1/2(0) + b
2 = b Now plug it in:
[tex]y=-\frac{1}{2}x+2[/tex]
Answer: y = -x/2 + 2
Step-by-step explanation:
The equation of a line given two points , is calculated by the formula :
[tex]\frac{y-y_{1}}{x - x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 0
[tex]y_{1}[/tex] = 1
[tex]y_{2}[/tex] = 2
substituting the values , we have
[tex]\frac{y-1}{x-2}[/tex] = [tex]\frac{2-1}{0-2}[/tex]
[tex]\frac{y-1}{x-2}[/tex] = [tex]\frac{1}{-2}[/tex]
-2(y-1) = x-2
-2y + 2 = x - 2
-2y = x - 2 - 2
-2y = x - 4
writing the equation in slope intercept form , we have
y = -x/2 + 2
