Find the x-intercept and the y-intercept of the graph of the equation.
6x + 2y = 24
To find the x-intercept, we need to let y = 0 and solve for x.
6x + 2(0) = 24
6x = 24
x = 4
Therefore, the x-intercept is 4.
To find the y-intercept, we need to let x = 0 and solve for y.
6(0) + 2y = 24
2y = 24
y = 12
Therefore, the y-intercept is 12.
Find the x- and y-intercepts of the line that passes through the given points.
(-5,-5), (5,-1)
To find the x-intercept, we set y = 0 and solve for x.
The two given points are (-5, -5) and (5, -1).
Let's use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope using the two given points.
m = (y2 - y1)/(x2 - x1)
m = (-1 - (-5))/(5 - (-5))
m = (-1 + 5)/(5 + 5)
m = 4/10
m = 2/5
Now, let's find the y-intercept (b) using one of the given points (-5, -5) and the slope (2/5).
y = mx + b
-5 = (2/5)(-5) + b
-5 = -2 + b
b = -5 + 2
b = -3
Therefore, the equation of the line passing through the given points is y = (2/5)x - 3.
Now we can find the x-intercept.
Let y = 0 and solve for x.
0 = (2/5)x - 3
3 = (2/5)x
x = 3(5/2)
x = 15/2
x = 7.5
Therefore, the x-intercept is 7.5.
To summarize:
The x-intercept is 7.5 and the y-intercept is -3.
Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-8,3); m = 6
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Using the given point (-8, 3) and slope m = 6, we can substitute the values into the equation:
y - 3 = 6(x - (-8))
Simplifying this equation, we get:
y - 3 = 6(x + 8)
Now, we can distribute the 6 to both terms inside the parentheses:
y - 3 = 6x + 48
Finally, we can add 3 to both sides to isolate the y-term:
y = 6x + 51
Thus, the equation of the line in point-slope form is y = 6x + 51.
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Apologies for the mistake. Let me correct it.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Using the given point (-8, 3) and slope m = 6, we can substitute the values into the equation:
y - 3 = 6(x - (-8))
Simplifying this equation, we get:
y - 3 = 6(x + 8)
Now, we can distribute the 6 to both terms inside the parentheses:
y - 3 = 6x + 48
Finally, we can subtract 3 from both sides to isolate the y-term:
y = 6x + 45
Thus, the equation of the line in point-slope form is y = 6x + 45.