A line passes through the point 10,−1 and has a slope of 3/2.
Write an equation in slope-intercept form for this line.
y = m x + b
y = (3/2) x + b
-1 = (3/2)(10) + b
b = -16
y = (3/2) x -16
Why did the line go to the movies?
Because it wanted to see a "slope-flick"!
Ahem, jokes aside, to write an equation in slope-intercept form (y = mx + b) for this line, we can use the given point and slope.
The slope (m) is 3/2, and the given point is (10, -1).
Plugging in the values, we have:
y = (3/2)x + b
Now, we need to find the value of b. Let's use the given point (10, -1):
-1 = (3/2)(10) + b
Simplifying:
-1 = 15 + b
To solve for b, we subtract 15 from both sides:
b = -1 - 15
b = -16
Therefore, the equation in slope-intercept form is:
y = (3/2)x - 16
To write the equation in slope-intercept form, we need the slope (m) and the y-intercept (b).
Given that the slope is 3/2, we can substitute the slope (m) into the equation.
The equation for a line in slope-intercept form is:
y = mx + b
Substituting the given slope, we get:
y = (3/2)x + b
Now we need to find the y-intercept (b). The information given tells us that the line passes through the point (10, -1). We can substitute these coordinates into the equation above and solve for b.
-1 = (3/2)(10) + b
Now, let's solve for b:
-1 = 15 + b
Subtracting 15 from both sides:
-1 - 15 = b
-16 = b
So, the value of y-intercept (b) is -16.
Plugging this value of b into the equation, the final equation in slope-intercept form is:
y = (3/2)x - 16
To write an equation in slope-intercept form (y = mx + b), we need to determine the values of the slope (m) and the y-intercept (b).
Given that the line has a slope of 3/2, we can substitute this value for m in the equation:
y = (3/2)x + b
Next, we need to find the value of the y-intercept (b). To do this, we can substitute one point on the line into the equation and solve for b. The point given in the question is (10, -1), meaning x = 10 and y = -1. Plugging these values into the equation, we get:
-1 = (3/2)(10) + b
Now, let's simplify the equation:
-1 = 15 + b
To isolate b, we need to subtract 15 from both sides:
-1 - 15 = b
Simplifying further:
-16 = b
We have found that the value of the y-intercept (b) is -16. Now, we can substitute this value back into the equation to get the final equation in slope-intercept form:
y = (3/2)x - 16