Write the equation of the line that passes through the points (3, 6) and (4, 10). (5 points)
y = 4x − 6
y = x + 4
y = 2x + 4
y = -4x − 6
the slope is (10-6)/(4-3) = 4
The only choice with that slope is y = 4x-6
Equation of straight line in two point form:
y - y1 = ( y2 - y1 ) ( x - x1 ) / ( x2 - x1 )
In this case:
x1 = 3 , y1 = 6 , x2 = 4 , y2 = 10
y - y1 = ( y2 - y1 ) ( x - x1 ) / ( x2 - x1 )
y - 6 = ( 10 - 6 ) ( x - 3 ) / ( 4 - 3 )
y - 6 = 4 ( x - 3 ) / 1
y - 6 = 4 x - 12
Add 6 to both sides
y = 4 x - 6
What does it matter how many points you get for this question?
To find the equation of the line that passes through two given points, we can use the formula for the equation of a line, which is y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's find the slope (m) of the line using the two given points (3, 6) and (4, 10). The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the points into the formula, we have:
m = (10 - 6) / (4 - 3)
m = 4
Now that we have the slope (m), we can find the y-intercept (b) using any of the given points. Let's choose the first point (3, 6). Substituting the values into the equation y = mx + b, we have:
6 = 4(3) + b
6 = 12 + b
b = -6
So, the slope (m) is 4 and the y-intercept (b) is -6. Plugging these values into the equation y = mx + b, we get:
y = 4x - 6
Therefore, the equation of the line that passes through the points (3, 6) and (4, 10) is y = 4x - 6.