finding a equation in slope-intercept form. Through (-9, 2.5) and (-5, 4.5)
Y= -1/7X + 1.2
(Y2-Y1)/(X2-X1) = slope
(4.5-2.5) / (-5+9) = slope call it m
then
(y-Y1)/(x-X1) = that same slope, m
so finally
y = Y1 + m (x-X1)
Is this correct? Ans. y=2x+20.5
To find the equation of a line in slope-intercept form, we need two pieces of information: the slope of the line (m) and the y-intercept (b).
The formula for the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Let's use the given points (-9, 2.5) and (-5, 4.5) to find the slope:
m = (4.5 - 2.5) / (-5 - (-9))
= 2 / 4
= 1/2
So, the slope (m) is 1/2.
Next, we can use the point-slope form of a linear equation to find the equation in slope-intercept form. The point-slope form is given by:
y - y₁ = m(x - x₁)
Now, substitute one of the points (-9, 2.5) into the equation:
y - 2.5 = (1/2)(x - (-9))
y - 2.5 = (1/2)(x + 9)
y - 2.5 = (1/2)x + 9/2
To convert this equation into slope-intercept form (y = mx + b), isolate the y-term:
y = (1/2)x + 9/2 + 2.5
y = (1/2)x + 9/2 + 5/2
y = (1/2)x + 14/2
y = (1/2)x + 7
Therefore, the equation in slope-intercept form for the line passing through (-9, 2.5) and (-5, 4.5) is y = (1/2)x + 7.