-5x + 5y=25
-10x+5y=10
Graph the linear equation by writing both equations in the slope intercept form... I'm really struggling with this questions.. i have to fill in y=___x+_____
y=____x+_____
For both equations, move the x's to the opposite side and divide both sides by 5.
y = x + 5 for the first one.
y = 2x + 2 for the second one.
The lines intersect where
2x + 2 = x + 5, which is
x = 3. At that point, y = 8
Let's solve the system of equations step-by-step to find the slope-intercept form of each equation and then graph them.
Step 1: Solve the first equation for y:
-5x + 5y = 25
We can start by isolating the y term by adding 5x to both sides:
5y = 5x + 25
Step 2: Divide both sides of the equation by 5 to solve for y:
y = (5x + 25)/5
Simplifying further:
y = x + 5
Therefore, the first equation can be written in slope-intercept form as y = x + 5.
Now let's solve the second equation for y:
Step 1: -10x + 5y = 10
Start by isolating the y term by adding 10x to both sides:
5y = 10x + 10
Step 2: Divide both sides of the equation by 5 to solve for y:
y = (10x + 10)/5
Simplifying further:
y = 2x + 2
Therefore, the second equation can be written in slope-intercept form as y = 2x + 2.
Now that we have both equations in slope-intercept form, let's graph them.
The first equation, y = x + 5, has a y-intercept of 5 and a slope of 1 (since the coefficient of x is 1).
The second equation, y = 2x + 2, has a y-intercept of 2 and a slope of 2.
Now, on a graph paper, plot the y-intercepts first, which are (0, 5) for the first equation and (0, 2) for the second equation.
Then, use the slope to find another point on each line.
For the first equation, since the slope is 1, you can move one unit up and one unit to the right from the y-intercept, giving you another point on the line (1, 6).
For the second equation, since the slope is 2, you can move two units up and one unit to the right from the y-intercept, giving you another point on the line (1, 4).
Finally, connect the points on each line to complete the graph.
I hope this helps! Let me know if you need further assistance.
To write the equation in slope-intercept form (y=mx+b), you need to isolate y on one side of the equation.
First, let's solve the first equation, -5x + 5y = 25, for y:
-5x + 5y = 25
Rearrange the equation to get the coefficient of y by itself:
5y = 5x + 25
Divide both sides by 5 to isolate y:
y = x + 5
So, the equation in slope-intercept form is y = 1x + 5 or y = x + 5.
Now let's solve the second equation, -10x + 5y = 10:
-10x + 5y = 10
Rearrange the equation to get the coefficient of y by itself:
5y = 10x + 10
Divide both sides by 5 to isolate y:
y = 2x + 2
Therefore, the equation in slope-intercept form is:
y = x + 5
y = 2x + 2