1. write the equation in slope-intercept form. what are the slope and y-intercept?
-9x+10y=-9
2. what is the graph of the equation?
-5x+y=-3
please help on these a.s.a.p thansk guys
#1
-9x + 10y = -9
10y = 9x-9
y = 9/10 x - 9/10
since this is the slope-intercept form, I leave it to you to determine the slope and y-intercept.
#2
rearrange things to the form y = mx+b
and m is the slope
1. To write the equation -9x + 10y = -9 in slope-intercept form, we need to isolate y on one side of the equation. We can do this by performing the following steps:
-9x + 10y = -9
Rearrange the equation to isolate y:
10y = 9x - 9
Divide both sides by 10 to solve for y:
y = (9/10)x - 9/10
From this form, we can identify the slope and y-intercept:
The slope (m) is the coefficient of x, which is 9/10.
The y-intercept (b) is the constant term, which is -9/10.
2. To graph the equation -5x + y = -3, we also need to rewrite it in slope-intercept form:
-5x + y = -3
Rearrange the equation to isolate y:
y = 5x - 3
From this equation, we can identify the slope and y-intercept:
The slope (m) is the coefficient of x, which is 5.
The y-intercept (b) is the constant term, which is -3.
To graph the equation, start by plotting the y-intercept at -3 on the y-axis. Then, use the slope to find additional points. Since the slope is 5, for every increase of 1 in the x-coordinate, the y-coordinate will increase by 5. So, plot another point at (1, 2) and connect the two points with a straight line.
The graph of the equation -5x + y = -3 will be a straight line passing through the points (-3, -3), (0, -3), and (1, 2).
To write the equation in slope-intercept form and find the slope and y-intercept, follow these steps for question 1:
Step 1: Start with the given equation: -9x + 10y = -9.
Step 2: To write the equation in slope-intercept form, solve for y. First, add 9x to both sides to isolate the term with y:
-9x + 9x + 10y = 9x - 9.
This simplifies to:
10y = 9x - 9.
Step 3: Divide both sides of the equation by 10 to solve for y:
(10y) / 10 = (9x - 9) / 10.
This gives us:
y = (9/10)x - 9/10.
Now we have the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The slope in this equation is the coefficient of x, which is 9/10.
The y-intercept is the constant term, -9/10.
For question 2, to graph the equation -5x + y = -3, follow these steps:
Step 1: Start by rewriting the equation in slope-intercept form. To do this, solve for y:
-5x + y = -3.
Add 5x to both sides:
y = 5x - 3.
Step 2: Now we can see that the equation has a slope of 5 and a y-intercept of -3.
Step 3: On a coordinate plane, plot the y-intercept, which is the point (0, -3).
Step 4: Use the slope to find additional points. The slope of 5 means that for every increase of 1 in x, y increases by 5. In other words, the slope tells us that we can move 1 unit to the right and 5 units up to find the next point. So, from the y-intercept point (0, -3), move 1 unit to the right, which brings you to the point (1, 2). Repeat the process and find the next point: from (1, 2), move 1 unit to the right and 5 units up to reach the point (2, 7).
Step 5: Plot the additional points (1, 2) and (2, 7) on the graph.
Step 6: Connect the points with a straight line. This line represents the graph of the equation -5x + y = -3.
Note: If you need more points to draw the line accurately, repeat the process of moving 1 unit right and 5 units up from any of the plotted points.