Respuesta :
Answer
The equation of our line is y = 8x - 3
Explanation
The slope-intercept form of writing the equation of the straight line is given as
y = mx + c
where
y = y-coordinate of any point on the line
m = slope of the line
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line; the value of y when x = 0.
To write this equation, we first compute the slope of the line
The slope of a line with two points on the line with the coordinates (x₁, y₁) and (x₂, y₂) given is calculated as
[tex]\text{Slope = }\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) is (1/2, 1) and (1, 5)
y₂ = 5
y₁ = 1
x₂ = 1
x₁ = (1/2) = 0.5
[tex]\text{Slope = }\frac{5-1}{1-0.5}=\frac{4}{0.5}=8[/tex]So, the slope of this line = 8
The equation of the line is then
y = 8x + c
We can now solve for the y-intercept by taking any of the two points given
Using (1, 5), x = 1, y = 5
y = 8x + c
5 = 8(1) + c
5 = 8 + c
c = 5 - 8 = -3
Hence, the equation of our line is y = 8x - 3
Hope this Helps!!!
