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 6/5; slope: 5/2; y-intercept: -6/5
c) π¦ =-5/2π₯ + 6; slope: -5/2; y-intercept: 6
d) π¦ =-2/5π₯ + 6; slope: -2/5; y-intercept: 6
To write the equation 5π₯ β 2π¦ = 12 in slope-intercept form, we need to solve for y.
Start by isolating y:
-2π¦ = -5π₯ + 12
Next, divide both sides of the equation by -2 to solve for y:
π¦ = (5/2)π₯ - 6
Now we can see that the equation in slope-intercept form is π¦ = (5/2)π₯ - 6.
The slope is 5/2 and the y-intercept is -6.
Therefore, the correct answer is:
b) π¦ = (5/2)π₯ - 6; slope: 5/2; y-intercept: -6.
To write the equation in slope-intercept form, we need to solve for y. Let's rearrange the given equation:
5x - 2y = 12
Subtract 5x from both sides:
5x - 5x - 2y = 12 - 5x
-2y = -5x + 12
Now, divide the entire equation by -2:
y = (-5/-2)x + 12/-2
Simplifying further:
y = (5/2)x - 6
In the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. From the equation y = (5/2)x - 6, we can see that the slope is 5/2 and the y-intercept is -6.
Therefore, the correct answer is:
a) π¦ = (5/2)π₯ β 6; slope: 5/2; y-intercept: -6