Solve by finding y and graph using the slope and y-intercept:
3x-y=1
x-y=3
3x-8=y
Use the point-slope form of an equation to write the following in slope intercept form:
m= 3 point: (4,2)
m= 3/8 point: (3,5)
3x-1=y
slope: 3; Y intercept:-1
x-3=y
slope: 1; Y intercept:-3
3x-8=y
slope: 3; Y intercept:-8
y-2=3(x-4)-->y=3x-10
y-5=3/8(x-3)-->y=3/8x-49/8
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
1. Solve the first equation for y:
3x - y = 1
y = 3x - 1
2. Substitute y in the second equation with 3x - 1:
x - (3x - 1) = 3
x - 3x + 1 = 3
-2x + 1 = 3
-2x = 3 - 1
-2x = 2
x = -1
3. Substitute the value of x into the first equation to find y:
3(-1) - y = 1
-3 - y = 1
-y = 1 + 3
-y = 4
y = -4
So the solution to the system of equations is x = -1 and y = -4.
To graph the equations using slope and y-intercept:
1. Equation 1: y = 3x - 1
The slope is 3, and the y-intercept is -1. To graph, start with the y-intercept (0, -1), plot this point, and then use the slope to find other points. The slope of 3 means that for every increase of 1 in the x-value, the y-value increases by 3. So starting from (0, -1), you can go up 3 units and to the right 1 unit to get another point, and so on.
2. Equation 2: y = x - 3
The slope is 1, and the y-intercept is -3. Follow the same process as above to graph this equation.
3. Equation 3: y = 3x - 8
Again, the slope is 3, and the y-intercept is -8. Follow the same process as above to graph this equation.
To write the equation in slope-intercept form from the given point and slope:
1. Equation 1: m = 3, point (4, 2)
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We have m = 3, and we need to find b. Using the point (4, 2), we can substitute the values into the equation and solve for b:
2 = 3 * 4 + b
2 = 12 + b
b = 2 - 12
b = -10
So, the equation in slope-intercept form is y = 3x - 10.
2. Equation 2: m = 3/8, point (3, 5)
Using the same process as above, substitute the values into the equation to solve for b:
5 = (3/8) * 3 + b
5 = 9/8 + b
b = 5 - 9/8
b = 40/8 - 9/8
b = 31/8
Therefore, the equation in slope-intercept form is y = (3/8)x + 31/8.