Write the equation in slope-intercept form and correctly list the slope and y-intercept.
5π₯ β 2π¦ = 12
a) π¦ = ; slope: ; y-intercept:
5
2
π₯ β 6
5
2 β 6
b) π¦ = ; slope: ; y-intercept:
5
2
π₯ β 6 β 6
5
2
c) π¦ =β ; slope: ; y-intercept:
5
2
π₯ β 6 β
5
2 β 6
d) π¦ =β ; slope: ; y-intercept:
5
2
π₯ + 6 β
5
2
6
a) π¦ = 5/2π₯ β 6; slope: 5/2; y-intercept: -6
b) π¦ = 5/2π₯ β 6; slope: 5/2; y-intercept: -6
c) π¦ = -5/2π₯ + 6; slope: -5/2; y-intercept: 6
d) π¦ = -5/2π₯ - 6; slope: -5/2; y-intercept: -6
To write the equation in slope-intercept form, we need to isolate the variable, y.
Let's start by rearranging the equation:
5π₯ β 2π¦ = 12
Subtract 5π₯ from both sides:
-2π¦ = -5π₯ + 12
Now, divide both sides by -2 to solve for y:
π¦ = (-5π₯ + 12) / -2
Simplifying further:
π¦ = -5/2π₯ - 6
So, the equation in slope-intercept form is:
π¦ = -5/2π₯ - 6
The slope is -5/2 and the y-intercept is -6.
Therefore, the correct answer is:
b) π¦ = -5/2π₯ - 6 ; slope: -5/2 ; y-intercept: -6
To write the equation in slope-intercept form (π¦ = ππ₯ + π), we need to isolate π¦ on one side of the equation.
Given equation: 5π₯ β 2π¦ = 12
Step 1: Move the π¦ term to the other side of the equation by subtracting 5π₯ from both sides:
-2π¦ = -5π₯ + 12
Step 2: Divide the entire equation by -2 to solve for π¦ and get the slope-intercept form:
π¦ = (-5/2)π₯ + (12/-2)
Simplifying the equation gives us:
π¦ = (-5/2)π₯ - 6
From the slope-intercept form, we can identify the slope (π) and the y-intercept (π).
The slope is the coefficient of π₯, which is -5/2.
The y-intercept is the constant term, which is -6.
Therefore, the correct answer is:
b) π¦ = (-5/2)π₯ - 6; slope: -5/2; y-intercept: -6