Respuesta :
Answer
The point-slope form of the equation of this line is
(y - (-45)) = 2.5 (x - 0)
y + 45 = 2.5x
OR
(y - (-25)) = 2.5 (x - 8)
y + 25 = 2.5x - 20
The slope-y intercept form of the equation of this line is
y = 2.5x - 45
Explanation
The point-slope form of the equation of a straight line is given as
(y - y₁) = m(x - x₁)
where
(x, y) represents the coordinates of any point on the line.
m = slope of the line.
(x₁, y₁) reresents the coordinates of a point given that the line passes through.
To write this form of the equation of a straight line, we need to just compute the slope of the line.
The slope of a straight line is given 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 (0. -45) and (8, -25) respectively.
x₁ = 0
y₁ = -45
x₂ = 8
y₂ = -25
[tex]\text{Slope =}\frac{-25-(-45)}{8-0}=\frac{-25+45}{8}=\frac{20}{8}=2.5[/tex]Using the first given point, (0, -45), to write the point-slope form of the equation of the line,
(y - (-45)) = 2.5 (x - 0)
y + 45 = 2.5x
The slope-y intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a 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.
And we can obtain this from the point-slope form by simply simplifying
(y - (-45)) = 2.5 (x - 0)
y + 45 = 2.5x
y = 2.5x - 45
Hope this Helps!!!
