Please help me with this question
Q:For each line,determine the x-intersept,the y-intersept,and the slope
a) 2x-5y+10=0 b)4x+y-12=0
please explain carefully , I'm dumb...
thank you
x-intercept means when the line intersect with the x-axis, at that point the value of y is 0.
y-intercept is the other way around, so the value of x = 0
so for you question:
1) x-intercept when y=0, so you just need to substitute y = 0 to the equations and solve for x.
2) y-intercept when x = 0, so substitute x = 0 to the equations and solve for y.
a) x-intercept: y = 0
2x - 5y +10 = 0
2x - 5*0 + 10 = 0
2x + 10 = 0
x = - 5
y - intercept: x = 0
2x - 5y + 10 = 0
2*0 - 5y + 10 = 0
-5y + 10 = 0
-5y = -10
y = 2
for b is similar to question a.
good luck
Don't worry, I'll explain it step by step so you can understand it easily.
To determine the x-intercept, we need to find the value of x when the line crosses the x-axis. To do this, we set y equal to zero and solve for x. Let's start with the first equation:
a) 2x - 5y + 10 = 0
Step 1: Set y = 0
2x - 5(0) + 10 = 0
2x + 10 = 0
Step 2: Solve for x
2x = -10
x = -10/2
x = -5
So, the x-intercept of the line a) is -5.
To determine the y-intercept, we need to find the value of y when the line crosses the y-axis. To do this, we set x equal to zero and solve for y.
Step 1: Set x = 0
2(0) - 5y + 10 = 0
-5y + 10 = 0
Step 2: Solve for y
-5y = -10
y = -10/-5
y = 2
So, the y-intercept of the line a) is 2.
Finally, to determine the slope, we need to rearrange the equation to be in slope-intercept form (y = mx + b), where m is the slope. Let's rearrange the equation a) to find the slope:
2x - 5y + 10 = 0
Step 1: Move 10 to the other side of the equation
2x - 5y = -10
Step 2: Solve for y
-5y = -2x - 10
y = (2/5)x + 2/5
Now we have y = (2/5)x + 2/5. The equation is now in slope-intercept form, where the coefficient of x (2/5) is the slope.
So, the slope of line a) is 2/5.
Let's now move on to the second equation:
b) 4x + y - 12 = 0
Following the same steps as above, we can determine the x-intercept, y-intercept, and slope for line b):
Step 1: Set y = 0
4x + 0 - 12 = 0
4x - 12 = 0
Step 2: Solve for x
4x = 12
x = 12/4
x = 3
So, the x-intercept of the line b) is 3.
Step 3: Set x = 0
4(0) + y - 12 = 0
y - 12 = 0
Step 4: Solve for y
y = 12
So, the y-intercept of the line b) is 12.
Step 5: Rearrange the equation to slope-intercept form
4x + y - 12 = 0
y = -4x + 12
Now we have y = -4x + 12. The coefficient of x (-4) is the slope.
So, the slope of line b) is -4.
I hope this explanation helps! Let me know if you have any more questions.