Respuesta :
First you'll find the equation of the graphed line in slope-intercept form, y = mx+b, and then from there we'll convert it into standard form, ax+by = c.
To find the slope of the line you could either use the two points on the line or just look and see.
Start from the point farther down, the point on (5,0). Look and see how many units it takes to go up/down to where the point on (0,3) is.
If it goes up, then you are at a positive slope so far. If it goes down, then you are at a negative slope so far. It takes 3 units UP (positive) to go onto the line that (0,3) is on.
Now see how far does it take to go left/right to where the point on (0,3) is. If you have to go left, that means you have a negative; if it goes right then you have a positive. It takes 5 units LEFT (negative) to where (0,3) is.
A positive (up) and a negative (left) make a negative, so your slope is how many units it took to go vertically/how many units it took to go horizontally.
Your slope is -3/5.
Now to solve for b, or the y-intercept, you can look on the graph to see where the point lies on the y-axis (vertical). The point lies on 3 on the y-axis, so your y-intercept is 3.
Since you have the slope and can see the y-intercept of the graphed line, you can make the equation y = mx+b by plugging in -3/5 for the slope and plugging in 3 for b (y-intercept).
y = (-3/5)x+(3)
Remove the parentheses: y = -3/5x+3.
Now to convert from slope-intercept form into standard form, you will have to move everything to the left side and leave only b, or 3.
Add -3/5x to both sides.
3/5x+y = 3
You can't have a fraction in standard form, so multiply everything in the equation by 5.
3x+5y = 15
Answer is:
C. 3x+5y = 15
The equation of the graphed line written in slope-intercept form (standard form) is 3x+5y = 15.
What is the Slope-Intercept form?
The graphed line in slope-intercept form, y = mx + b
Convert it into the standard form of the equation, ax + by = c.
Let the points be (0, 3) and (5,0).
A positive (up) and a negative (left) make a negative.
Slope exists how many units it brought to go vertically or horizontally.
Slope exists -3/5.
Now to solve for b, or the y-intercept, you can look at the graph to see where the point lies on the y-axis (vertical).
The point lies on 3 on the y-axis, so your y-intercept exists at 3.
The y-intercept in slope-intercept form, y = mx + b
where, m = -3/5
y = (-3/5)x + (3)
Remove the parentheses: y = -3/5x+3.
Now to convert from the slope-intercept form into standard form,
Add -3/5x to both sides.
3/5x + y = -3/5x + 3 - 3/5x.
3/5x + y = 3
Multiply everything in the equation by 5, then we get.
3x + 5y = 15
Therefore, the correct answer is option (c), 3x+5y=15
To learn more about slope-intercept form
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